Open Problems in Sublinear Algorithms - User contributions [en]

Open Problems:95

2019-08-26T20:40:07Z

Ccanonne:

{{Header
|source=wola19
|who=Oliver Gebhard
}}
In (non-adaptive) quantitative group testing, one has a population of $n$ individuals, among which $k=n^c$ (for some constant $c\in(0,1)$) are sick. The goal is to identify the $k$ sick individuals by performing $m$ non-adaptive tests. In each test, one specifies a subset $S\subseteq [n]$ and learns whether $S$ contains one or more sick individuals.

By a counting argument, one gets a lower bound of $m = \Omega\bigl( \frac{k}{\log k}\log \frac{n}{k} \bigr)$ tests; however, the best known upper bound is $m = O( k\log \frac{n}{k} )$.

'''Question:''' Can one get rid of the $\log k$ factor in the lower bound; or, conversely, improve the upper bound to match it?

Workshops:WOLA 2019

2019-08-26T20:06:24Z

Ccanonne:

{{DISPLAYTITLE:Workshop on Local Algorithms 2019 at ETH Zurich}}
The 3rd Workshop on Local Algorithms was held at ETH Zurich in July of 2019. This list contains open problems suggested by participants during the open problems session. The list was written by Clément Canonne. More information about the workshop can be found at [https://people.inf.ethz.ch/gmohsen/WOLA19/ the workshop webpage].

== Links ==
* [https://people.inf.ethz.ch/gmohsen/WOLA19/ Workshop webpage]

== Open Problems ==
*{{ProblemLink|95}}
*{{ProblemLink|96}}
*{{ProblemLink|97}}
*{{ProblemLink|98}}
*{{ProblemLink|99}}
*{{ProblemLink|100}}
*{{ProblemLink|101}}
*{{ProblemLink|102}}

Open Problems:91

2019-08-20T04:32:21Z

Ccanonne:

{{Header
|source=warwick18
|who=Robert Krauthgamer
}}
Informally, a cut-sparsifier of a hypergraph $H$ is a sparse hypergraph $H'$ on the same vertex set, whose cuts approximate those of $H$. The two “competing” quantities are the approximation factor and the size of the sparsifier $H'$ (for worst-case hypergraph $H$ on $n$ vertices). More formally, Let $H=(V,E,w)$ be an edge-weighted hypergraph. The weight of the cut $(S,\bar S)$ (i.e., for nontrivial $S\subset V$) is defined as
$$
w_H(S,\bar S) := \sum_{e\in E: e\cap S\neq\emptyset, e\cap\bar S \neq\emptyset} w(e) .
$$
A $(1+\epsilon)$-cut-sparsifier of $H$ is a hypergraph $H'=(V,E',w')$ (on the same vertex-set) such that
$$
\forall S\subset V, \qquad
w_{H'}(S,\bar S) \in (1\pm\epsilon) w_H(S,\bar S) .
$$

'''Question:''' Is it true that for every $n$-vertex hypergraph $H$ and every $\epsilon\in (0,1/2)$, there is a $(1+\epsilon)$-cut-sparsifier $H'$ with at most $O(n/\epsilon^2)$ edges?

'''Upper bound:''' The known bound is $O(n^2/\epsilon^2)$ due to Kogan and Krauthgamer {{cite|KoganK-15}}. It is based on the sparsification method of Benczur and Karger {{cite|BenczurK-96}}. Another proof can be derived from a paper of Newman and Rabinovich {{cite|NewmanR-13}}.

'''Special cases:''' The current upper bound $O(n^2/\epsilon^2)$ can be refined in terms of $\rank(H) := \max_{e\in E} |e| \leq n$. When $\rank(H)=2$ (i.e., ordinary graphs where all edges have cardinality 2), there always exists a sparsifier $H'$ of size $O(n/\epsilon^2)$ {{cite|BatsonSS-14}}.
This bound easily extends to $\rank(H)=3$, because every hyperedge in $H$ can be replaced by a triangle (3 edges of cardinality 2) with edge weights $1/2$. For intermediate values of $\rank(H)$, the known upper bound is $O((\rank(H)+\log n) n/\epsilon^2)$ {{cite|KoganK-15}}.
Another family of hypergraphs that admits an improved bound is when for every two vertices $u,v\in V$, there is at most one edge $e\in E$ containing both $u$ and $v$; see the thesis of Pogrow {{cite|Pogrow-17}}. Note that this family clearly contains all ordinary graphs.

'''Lower bound:''' The only known lower bound is for ordinary graphs, and shows that (for every $n$ and $\epsilon>1/\sqrt{n}$) there is a hypergraph $H$ with $\rank(H)=2$, such that every $(1+\epsilon)$-cut-sparsifier must have $\Omega(n/\epsilon^2)$ edges {{cite|AndoniCKQWZ-16}}. A different, much simpler proof was devised by Carlson, Kolla, Srivastava, and Trevisan {{cite|CarlsonKST-17}}. Thus, there is a large gap between the upper bound $O_\epsilon(n^2)$ and the lower bound $\Omega_\epsilon(n)$ (this notation omits dependence on $\epsilon$).

'''Remark:''' The above considers the number of hyperedges to be the size measure. An alternative measure is the total size of all hyperedges, i.e., $\sum_{e\in E} |e|$. The current upper bound on the total size of the sparsifier is $O_\epsilon(n^3)$, because every hyperedge has size at most $n$, and the lower bound is $\Omega_\epsilon(n)$ (coming from ordinary graphs), hence the gap here is even larger.

Open Problems:90

2019-08-20T04:31:24Z

Ccanonne:

{{Header
|source=warwick18
|who=Clément Canonne
}}
In the dense graph model of property testing (where the testing algorithm is granted query access to the adjacency matrix of an unknown $n$-node graph, and the distance measure is the fraction of entries of this matrix that needs to be changed for the graph to satisfy the property), ''testability'' was originally defined as meaning “a number of queries depending only on the proximity parameter $\varepsilon$ (but not $n$).” Many properties, such as graph partition properties, triangle-freeness, and more generally $H$-freeness, are known to be testable with a constant number of queries in this sense. Moreover, we now have a full characterization of the graph properties that admit $O_\varepsilon(1)$-query testers {{Cite|AlonFNS-09}}.

These kinds of testers are, however, typically obtained via regularity lemmata, such as Szemerédi's Regularity Lemma, and the “constant” query complexity is often superpolynomial in $1/\varepsilon$ (more often than not, it is even a tower of 2's of height $\operatorname{poly}(1/\varepsilon)$). This is not an oversight: triangle freeness, for instance, provably does ''not'' have any tester with query complexity $\operatorname{poly}(1/\varepsilon)$ {{Cite|Alon-02}}. See for instance Section 8.5 of Goldreich's book {{Cite|Goldreich-17}} for a summary of the state of the art in property testing in the dense graph model.

Nevertheless, nothing ''a priori'' precludes these properties from having testers with query complexity $\sqrt{n}\operatorname{poly}(1/\varepsilon)$, $\operatorname{poly}(\log n, 1/\varepsilon)$, or even $\operatorname{poly}(\log^* n, 1/\varepsilon)$. What is the best possible tradeoff between $n$ and $\varepsilon$? Note that ''every'' property trivially has a tester with query complexity $O(n^2)$, so the question is how far down this dependence on $n$ can be brought while keeping a reasonable dependence on $\varepsilon$.

'''Concrete instance of the problem:''' Is there a $\operatorname{poly}(\log n, 1/\varepsilon)$-query tester for triangle freeness in the dense graph model?

Open Problems:94

2019-08-07T22:13:25Z

Ccanonne:

{{Header
|title=Ads, Impressions, and Statistics
|source=warwick18
}}

1. Consider the problem of reporting statistics about online ads to the advertisers that pay for them. Advertisers may wish to know how many unique people matching some demographic conditions have seen an ad at a particular time range. There are many ads and many demographic conditions and time ranges; and the service provider should be able to accurately answer any possible query over ads, demographics, and time. In other words, it’s an [https://en.wikipedia.org/wiki/OLAP_cube OLAP cube] problem where the aggregate is ''distinct count'' rather than ''sum''. How can one construct a sketch that will provide estimates with "good" errors that solves this with, say, $O(1)$ time complexity per query? Loosely speaking, "good" here means every query for an ad (without demographic conditions) has good relative error and any query that has a high count should have good relative error.

2. Suppose a company tracks an important high level metric ''(e.g., total network traffic)'' that is the sum of a metric over many discrete categories ''(e.g., country, device, network provider, etc.)''. When that metric changes in an unexpected way, it wishes to figure out what combinations of categories are driving that change. How can one find a small set of combination of categories that explains most of the change and can be described succinctly? Can this be done in real-time so that a streaming sketch can keep track of the appropriate approximate aggregates and the search for a succinct description of category can be done in "reasonable" time?

Open Problems:94

2019-08-07T22:11:19Z

Ccanonne: Created page with "{{Header |title=Ads, Impressions, and Statistics&action=submit |source=warwick18 }} 1. Consider the problem of reporting statistics about online ads to the advertisers that..."

{{Header
|title=Ads, Impressions, and Statistics&action=submit
|source=warwick18
}}

1. Consider the problem of reporting statistics about online ads to the advertisers that pay for them. Advertisers may wish to know how many unique people matching some demographic conditions have seen an ad at a particular time range. There are many ads and many demographic conditions and time ranges; and the service provider should be able to accurately answer any possible query over ads, demographics, and time. In other words, it’s an OLAP cube problem where the aggregate is ''distinct count'' rather than ''sum''. How can one construct a sketch that will provide estimates with "good" errors that solves this with, say, $O(1)$ time complexity per query? Loosely speaking, "good" here means every query for an ad (without demographic conditions) has good relative error and any query that has a high count should have good relative error.

2. Suppose a company tracks an important high level metric (e.g. Total network traffic) that is the sum of a metric over many discrete categories (e.g., country, device, network provider, etc.). When that metric changes in an unexpected way, it wishes to figure out what combinations of categories are driving that change. How can one find a small set of combination of categories that explains most of the change and can be described succinctly? Can this be done in real-time so that a streaming sketch can keep track of the appropriate approximate aggregates and the search for a succinct description of category can be done in "reasonable" time?

Waiting

2019-08-07T22:07:51Z

Ccanonne:

{{DISPLAYTITLE:Waiting Room}}
Submitting a new problem:
# Make sure your problem is not yet on [[Open_Problems:By_Number|the list]].
# Edit this page to add <code><nowiki>*[[Waiting:Your Problem Name|]]</nowiki></code> at the bottom. This will create a link to a page for your new problem.
# Copy the content of [[Waiting:Sample Problem]] and use it as a starting point.
# Take your time editing the problem. See also [[Editing| the page with editing guidelines]].
# Once you are satisfied with the quality of the writeup, send an email to [mailto:admin@sublinear.info admin@sublinear.info].

== Problems in Preparation ==

*[[Waiting:Sample Problem|Sample Problem]] ← Please do not remove or edit!

The Warwick workshop:

*[[Waiting:Dense_Graph_Property_Testing_Tradeoffs]]
*[[Waiting:Cut-Sparsification_of_Hypergraphs]]
*[[Waiting:Streaming_Algorithms_for_Approximating_the_Number_of_Subgraphs]]
*[[Waiting:Heavy_Hitters_and_Other_Problems_in_Streaming]]
*[[Waiting:Ads_Impressions_and Statistics]]

WoLA'19:
*[[Waiting:Non-Adaptive Group Testing]]
*[[Waiting:Identity Testing Up to Coarsenings]]
*[[Waiting:Local Computation Algorithm for MIS]]
*[[Waiting:Estimating a Graph's Degree Distribution]]
*[[Waiting:Vertex-Distribution-Free Graph Testing]]
*[[Waiting:Effective Support Size Estimation in the Dual Model]]
*[[Waiting:Vertex connectivity in the LOCAL model]]
*[[Waiting:Making edges happy in the LOCAL model]]

Waiting

2019-08-07T22:07:45Z

Ccanonne:

{{DISPLAYTITLE:Waiting Room}}
Submitting a new problem:
# Make sure your problem is not yet on [[Open_Problems:By_Number|the list]].
# Edit this page to add <code><nowiki>*[[Waiting:Your Problem Name|]]</nowiki></code> at the bottom. This will create a link to a page for your new problem.
# Copy the content of [[Waiting:Sample Problem]] and use it as a starting point.
# Take your time editing the problem. See also [[Editing| the page with editing guidelines]].
# Once you are satisfied with the quality of the writeup, send an email to [mailto:admin@sublinear.info admin@sublinear.info].

== Problems in Preparation ==

*[[Waiting:Sample Problem|Sample Problem]] ← Please do not remove or edit!

The Warwick workshop:

*[[Waiting:Dense_Graph_Property_Testing_Tradeoffs]]
*[[Waiting:Cut-Sparsification_of_Hypergraphs]]
*[[Waiting:Streaming_Algorithms_for_Approximating_the_Number_of_Subgraphs]]
*[[Waiting:Heavy_Hitters_and_Other_Problems_in_Streaming]]
*[[Waiting: Ads_Impressions_and Statistics]]

WoLA'19:
*[[Waiting:Non-Adaptive Group Testing]]
*[[Waiting:Identity Testing Up to Coarsenings]]
*[[Waiting:Local Computation Algorithm for MIS]]
*[[Waiting:Estimating a Graph's Degree Distribution]]
*[[Waiting:Vertex-Distribution-Free Graph Testing]]
*[[Waiting:Effective Support Size Estimation in the Dual Model]]
*[[Waiting:Vertex connectivity in the LOCAL model]]
*[[Waiting:Making edges happy in the LOCAL model]]

Open Problems:93

2019-08-07T22:06:14Z

Ccanonne:

{{Header
|title=Locally Private Heavy Hitters and Other Problems in Streaming
|source=warwick18
|who=Graham Cormode
}}

The model of Local Differential Privacy (LDP) asks for protocols for information release, so that each user's output meets a differential privacy guarantee. A basic primitive is based on a simple coin-flipping method: when users have one private bit of information, they toss a biased coin, so that with probability $p > 1/2$ the true value is released, and with probability $1-p$ the complement is released. The privacy level is quantified by $\varepsilon = \ln(p/1-p)$.

There has been considerable progress in this area by adapting ideas familiar to the sublinear community: dimensionality reduction, sketching, basis transforms, hashing techniques etc. For example, recent work of Bun, Nelson, and Stemmer {{Cite|BunNS-18}} adapts methods for heavy hitters to the LDP model.

Consequently, the open problem is to address other questions in the LDP model, and to provide lower bounds on what can be achieved under this notion of privacy.

Bibliography

2019-08-07T22:05:10Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14|Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BunNS-18|Mark Bun, Jelani Nelson, and Uri Stemmer. ''Heavy Hitters and the Structure of Local Privacy.'' In ''PODS'', pages 435-447, 2018.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages 449–458. 2018.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|ForsterY-19|Sebastian Forster and Liu Yang. ''A faster local algorithm for detecting bounded-size cuts with applications to higher-connectivity problems.'' In ''CoRR,'' abs/1904.08382, 2019.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|Goldreich-19a|Oded Goldreich. ''Testing graphs in vertex-distribution-free models.'' In ''STOC'', pages 527–534, 2019.}}

{{bibentry|Goldreich-19b|Oded Goldreich. ''On the complexity of estimating the effective support size.'' Electronic Colloquium on Computational Complexity (ECCC), 26:88, 2019.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GoldreichGR-98|Oded Goldreich, Shafi Goldwasser, and Dana Ron. ''Property testing and its connection to learning and approximation.'' J. ACM, 45(4):653–750, 1998.}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NanongkaiSY-19a|Danupon Nanongkai, Thatchaphol Saranurak, and Sorrachai Yingchareonthawornchai. ''Breaking quadratic time for small vertex connectivity and an approximation scheme.'' In ''STOC'', pages 241–252, 2019.}}

{{bibentry|NanongkaiSY-19b|Danupon Nanongkai, Thatchaphol Saranurak, and Sorrachai Yingchareonthawornchai. ''Computing and testing small vertex connectivity in near-linear time and queries.'' In ''CoRR,'' abs/1905.05329, 2019.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Open Problems:93

2019-08-07T22:03:46Z

Ccanonne: Created page with "The model of Local Differential Privacy (LDP) asks for protocols for information release, so that each user's output meets a differential privacy guarantee. A basic primitive..."

The model of Local Differential Privacy (LDP) asks for protocols for information release, so that each user's output meets a differential privacy guarantee. A basic primitive is based on a simple coin-flipping method: when users have one private bit of information, they toss a biased coin, so that with probability $p > 1/2$ the true value is released, and with probability $1-p$ the complement is released. The privacy level is quantified by $\varepsilon = \ln(p/1-p)$.

There has been considerable progress in this area by adapting ideas familiar to the sublinear community: dimensionality reduction, sketching, basis transforms, hashing techniques etc. For example, recent work of Bun, Nelson, and Stemmer {{Cite|BunNS-18}} adapts methods for heavy hitters to the LDP model.

Consequently, the open problem is to address other questions in the LDP model, and to provide lower bounds on what can be achieved under this notion of privacy.

Waiting

2019-08-07T21:59:59Z

Ccanonne:

{{DISPLAYTITLE:Waiting Room}}
Submitting a new problem:
# Make sure your problem is not yet on [[Open_Problems:By_Number|the list]].
# Edit this page to add <code><nowiki>*[[Waiting:Your Problem Name|]]</nowiki></code> at the bottom. This will create a link to a page for your new problem.
# Copy the content of [[Waiting:Sample Problem]] and use it as a starting point.
# Take your time editing the problem. See also [[Editing| the page with editing guidelines]].
# Once you are satisfied with the quality of the writeup, send an email to [mailto:admin@sublinear.info admin@sublinear.info].

== Problems in Preparation ==

*[[Waiting:Sample Problem|Sample Problem]] ← Please do not remove or edit!

The Warwick workshop:

*[[Waiting:Dense_Graph_Property_Testing_Tradeoffs]]
*[[Waiting:Cut-Sparsification_of_Hypergraphs]]
*[[Waiting:Streaming_Algorithms_for_Approximating_the_Number_of_Subgraphs]]
*[[Waiting:Heavy_Hitters_and_Other_Problems_in_Streaming]]

WoLA'19:
*[[Waiting:Non-Adaptive Group Testing]]
*[[Waiting:Identity Testing Up to Coarsenings]]
*[[Waiting:Local Computation Algorithm for MIS]]
*[[Waiting:Estimating a Graph's Degree Distribution]]
*[[Waiting:Vertex-Distribution-Free Graph Testing]]
*[[Waiting:Effective Support Size Estimation in the Dual Model]]
*[[Waiting:Vertex connectivity in the LOCAL model]]
*[[Waiting:Making edges happy in the LOCAL model]]

Open Problems:92

2019-08-07T21:57:17Z

Ccanonne: Created page with "{{Header |title=Streaming Algorithms for Approximating the Number of $H$-Subgraphs |source=warwick18 |who=He Sun }} Designing a streaming algorithm that approximately computes..."

{{Header
|title=Streaming Algorithms for Approximating the Number of $H$-Subgraphs
|source=warwick18
|who=He Sun
}}
Designing a streaming algorithm that approximately computes the number
of a subgraph is an intensively studied problem with applications in
data mining and database theory. The space complexities of such
algorithms are usually a function of $\#$H (the number of subgraph $H$), so
an algorithm gives a good approximation of $\#H$ in sublinear space only
if a reasonable lower bound of $\#H$ is known in advance, which is not
realistic for some scenarios. It’s practically interesting to study
the possibility of designing a multi-pass streaming algorithm which
gives a guaranteed approximation of $\#H$ and does not assume the
knowledge of a lower bound of $\#H$. Specifically, it is interesting to
see, for any algorithm that gives an $\alpha$-approximation of $\#H$, the
relationship needed among $\alpha$, the space complexity and the number
of passes (not necessarily a constant) that the algorithm needs to
read the input graph stream.

Waiting

2019-08-07T21:54:56Z

Ccanonne:

{{DISPLAYTITLE:Waiting Room}}
Submitting a new problem:
# Make sure your problem is not yet on [[Open_Problems:By_Number|the list]].
# Edit this page to add <code><nowiki>*[[Waiting:Your Problem Name|]]</nowiki></code> at the bottom. This will create a link to a page for your new problem.
# Copy the content of [[Waiting:Sample Problem]] and use it as a starting point.
# Take your time editing the problem. See also [[Editing| the page with editing guidelines]].
# Once you are satisfied with the quality of the writeup, send an email to [mailto:admin@sublinear.info admin@sublinear.info].

== Problems in Preparation ==

*[[Waiting:Sample Problem|Sample Problem]] ← Please do not remove or edit!

The Warwick workshop:

*[[Waiting:Dense_Graph_Property_Testing_Tradeoffs]]
*[[Waiting:Cut-Sparsification_of_Hypergraphs]]
*[[Waiting:Streaming_Algorithms_for_Approximating_the_Number_of_Subgraphs]]

WoLA'19:
*[[Waiting:Non-Adaptive Group Testing]]
*[[Waiting:Identity Testing Up to Coarsenings]]
*[[Waiting:Local Computation Algorithm for MIS]]
*[[Waiting:Estimating a Graph's Degree Distribution]]
*[[Waiting:Vertex-Distribution-Free Graph Testing]]
*[[Waiting:Effective Support Size Estimation in the Dual Model]]
*[[Waiting:Vertex connectivity in the LOCAL model]]
*[[Waiting:Making edges happy in the LOCAL model]]

Waiting

2019-08-07T21:54:36Z

Ccanonne:

{{DISPLAYTITLE:Waiting Room}}
Submitting a new problem:
# Make sure your problem is not yet on [[Open_Problems:By_Number|the list]].
# Edit this page to add <code><nowiki>*[[Waiting:Your Problem Name|]]</nowiki></code> at the bottom. This will create a link to a page for your new problem.
# Copy the content of [[Waiting:Sample Problem]] and use it as a starting point.
# Take your time editing the problem. See also [[Editing| the page with editing guidelines]].
# Once you are satisfied with the quality of the writeup, send an email to [mailto:admin@sublinear.info admin@sublinear.info].

== Problems in Preparation ==

*[[Waiting:Sample Problem|Sample Problem]] ← Please do not remove or edit!

The Warwick workshop:

*[[Waiting:Dense_Graph_Property_Testing_Tradeoffs]]
*[[Waiting:Cut-Sparsification_of_Hypergraphs]]
*[[Waiting:Streaming_Algorithms_for_Approximating_the_Number_of_$H$-subgraphs]]

WoLA'19:
*[[Waiting:Non-Adaptive Group Testing]]
*[[Waiting:Identity Testing Up to Coarsenings]]
*[[Waiting:Local Computation Algorithm for MIS]]
*[[Waiting:Estimating a Graph's Degree Distribution]]
*[[Waiting:Vertex-Distribution-Free Graph Testing]]
*[[Waiting:Effective Support Size Estimation in the Dual Model]]
*[[Waiting:Vertex connectivity in the LOCAL model]]
*[[Waiting:Making edges happy in the LOCAL model]]

Open Problems:102

2019-08-07T21:47:33Z

Ccanonne: Created page with "{{Header |title=Making edges happy in the LOCAL model |source=wola19 |who=Jukka Suomela }} In this question, the input is the underlying graph $G=(V,E)$, promised to have max..."

{{Header
|title=Making edges happy in the LOCAL model
|source=wola19
|who=Jukka Suomela
}}

In this question, the input is the underlying graph $G=(V,E)$, promised to have maximum degree at most $\Delta$, and the goal is to compute an orientation of the edges of $E$ which makes all edges "happy." Specifically, for any given orientation of the edges, the ''load'' of a node $v\in V$ is its number of incoming edges. An edge $e$ is then said to be ''happy'' if switching its orientation does not make it point to a smaller-node load.

One can show by a greedy argument that there always exists an orientation making all edges happy. Moreover, a surprising result established that, in the LOCAL model, such a configuration could be found in $\operatorname{poly}(\Delta)$ rounds, ''independent'' of the number of nodes $n$. However, the question of the dependence on $\Delta$ remains wide open, as even a $\operatorname{poly}\!\log(\Delta)$ upper bound is not ruled out.

'''Question:''' What is the right dependence on $\Delta$? Can one show ''any'' lower polynomial lower bound, e.g., $\Delta^{0.1}$, $\sqrt{\Delta}$, or $\Delta$?

Open Problems:101

2019-08-07T21:45:45Z

Ccanonne:

{{Header
|title=Vertex connectivity in the LOCAL model
|source=wola19
|who=Sorrachai Yingchareonthawornchai
}}

In this question, the input is the underlying graph $G=(V,E)$, as well as parameters $\nu,k$ and vertex $v\in V$. The goal is to output either $\bot$ or a subset $S\subseteq V$, such that

- if $\bot$ is the output, there is no $S$ such that $v\in S$ with $|S| \leq \nu$ and $|N(S)| < k$;

- if the output is a set $S$, then $|N(S)| < k$.

It is known that this problem can be solved with $O(\nu k)$ queries, and either time $O(\nu^{3/2} k)$ (deterministic) or $O(\nu k^2)$ (randomized) {{Cite|NanongkaiSY-19a|NanongkaiSY-19b|ForsterY-19}}.

'''Question:''' Can one achieve time $O(\nu k)$?

Bibliography

2019-08-07T21:44:29Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages 449–458. 2018.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|ForsterY-19|Sebastian Forster and Liu Yang. ''A faster local algorithm for detecting bounded-size cuts with applications to higher-connectivity problems.'' In ''CoRR,'' abs/1904.08382, 2019.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|Goldreich-19a|Oded Goldreich. ''Testing graphs in vertex-distribution-free models.'' In ''STOC'', pages 527–534, 2019.}}

{{bibentry|Goldreich-19b|Oded Goldreich. ''On the complexity of estimating the effective support size.'' Electronic Colloquium on Computational Complexity (ECCC), 26:88, 2019.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GoldreichGR-98|Oded Goldreich, Shafi Goldwasser, and Dana Ron. ''Property testing and its connection to learning and approximation.'' J. ACM, 45(4):653–750, 1998.}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NanongkaiSY-19a|Danupon Nanongkai, Thatchaphol Saranurak, and Sorrachai Yingchareonthawornchai. ''Breaking quadratic time for small vertex connectivity and an approximation scheme.'' In ''STOC'', pages 241–252, 2019.}}

{{bibentry|NanongkaiSY-19b|Danupon Nanongkai, Thatchaphol Saranurak, and Sorrachai Yingchareonthawornchai. ''Computing and testing small vertex connectivity in near-linear time and queries.'' In ''CoRR,'' abs/1905.05329, 2019.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Bibliography

2019-08-07T21:43:49Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages 449–458. 2018.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|ForsterY-19|Sebastian Forster and Liu Yang. ''A faster local algorithm for detecting bounded-size cuts with applications to higher-connectivity problems.'' In ''CoRR,'' abs/1904.08382, 2019.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|Goldreich-19a|Oded Goldreich. ''Testing graphs in vertex-distribution-free models.'' In ''STOC'', pages 527–534, 2019.}}

{{bibentry|Goldreich-19b|Oded Goldreich. ''On the complexity of estimating the effective support size.'' Electronic Colloquium on Computational Complexity (ECCC), 26:88, 2019.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GoldreichGR-98|Oded Goldreich, Shafi Goldwasser, and Dana Ron. ''Property testing and its connection to learning and approximation.'' J. ACM, 45(4):653–750, 1998.}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NanongkaiSY-19a|Danupon Nanongkai, Thatchaphol Saranurak, and Sorrachai Yingchareonthawornchai. ''Breaking quadratic time for small vertex connectivity and an approximation scheme.'' In ''STOC'', pages 241–252, 2019.}}

{{bibentry|NanongkaiSY-19b|Danupon Nanongkai, Thatchaphol Saranurak, and Sorrachai Yingchareonthawornchai. ''Computing and testing small vertex connectivity in near-linear time and queries.'' In ''CoRR,''
abs/1905.05329, 2019.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Open Problems:101

2019-08-07T21:40:32Z

Ccanonne: Created page with "{{Header |title=Effective Support Size Estimation in the Dual Model |source=wola19 |who=Sorrachai Yingchareonthawornchai }} In this question, the input is the underlying grap..."

{{Header
|title=Effective Support Size Estimation in the Dual Model
|source=wola19
|who=Sorrachai Yingchareonthawornchai
}}

In this question, the input is the underlying graph $G=(V,E)$, as well as parameters $\nu,k$ and vertex $v\in V$. The goal is to output either $\bot$ or a subset $S\subseteq V$, such that

- if $\bot$ is the output, there is no $S$ such that $v\in S$ with $|S| \leq \nu$ and $|N(S)| < k$;

- if the output is a set $S$, then $|N(S)| < k$.

It is known that this problem can be solved with $O(\nu k)$ queries, and either time $O(\nu^{3/2} k)$ (deterministic) or $O(\nu k^2)$ (randomized) {{Cite|NanongkaiSY-19a|NanongkaiSY-19b|ForsterY-19}}.

'''Question:''' Can one achieve time $O(\nu k)$?

Bibliography

2019-08-07T21:37:51Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
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{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages 449–458. 2018.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|Goldreich-19a|Oded Goldreich. ''Testing graphs in vertex-distribution-free models.'' In ''STOC'', pages 527–534, 2019.}}

{{bibentry|Goldreich-19b|Oded Goldreich. ''On the complexity of estimating the effective support size.'' Electronic Colloquium on Computational Complexity (ECCC), 26:88, 2019.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GoldreichGR-98|Oded Goldreich, Shafi Goldwasser, and Dana Ron. ''Property testing and its connection to learning and approximation.'' J. ACM, 45(4):653–750, 1998.}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Open Problems:100

2019-08-07T21:37:09Z

Ccanonne: Created page with "{{Header |title=Effective Support Size Estimation in the Dual Model |source=wola19 |who=Oded Goldreich }} For a probability distribution $p$ over a discrete domain $\Omega$, a..."

{{Header
|title=Effective Support Size Estimation in the Dual Model
|source=wola19
|who=Oded Goldreich
}}
For a probability distribution $p$ over a discrete domain $\Omega$, and a parameter $\varepsilon\in[0,1]$, denote by
\[
\operatorname{ess}_\varepsilon(p) \stackrel{\rm def}{=} \min\{ \operatorname{supp}(q) : \operatorname{d}_{\rm TV}(p,q) \leq \varepsilon \}
\]
the $\varepsilon$-effective suport size of $p$, i.e., the smallest possible support size of any distribution $\varepsilon$-close to $p$. This turns out to be a more robust and interesting measure in general than the support of $p$, which is $\operatorname{ess}_0(p) = \operatorname{supp}(p)$. In recent work, Goldreich {{Cite|Goldreich-19b}} focused on the query complexity of approximating the effective support size of a discrete distribution provided via two oracles: sampling ($\textsf{samp}_p$), and query access (to the probability mass function), $\textsf{eval}_p$. In particular, the goal is, given parameters $\varepsilon$ and $\beta>1$, to output an $f(\varepsilon,\beta,n)$-factor approximation of $\operatorname{ess}_{\varepsilon'}(p)$, for some $\varepsilon' \in [\varepsilon,\beta\varepsilon]$.

In the aforementioned work, algorithms are obtained achieving (for constant $\beta>1$)

- query complexity $\operatorname{poly}(1/\varepsilon)$ and approximation factor $f = O(\log\log\log\log(n/\varepsilon))$, that is, any constant number of iterated logarithms;

- query complexity $\operatorname{poly}(\log^\ast n, 1/\varepsilon)$ even for approximation factor $f = O(1)$;

where $n \stackrel{\rm def}{=} \operatorname{ess}_\varepsilon(p)$. (As well as several other results interpolating between the two extremes.)

'''Question:''' Can one get the best of both worlds, and get rid of the $\log^\ast n$ to obtain query complexity $\operatorname{poly}(1/\varepsilon)$ ''and'' constant approximation factor?

Bibliography

2019-08-07T21:37:03Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages 449–458. 2018.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-19a|Oded Goldreich. ''Testing graphs in vertex-distribution-free models.'' In ''STOC'', pages 527–534, 2019.}}

{{bibentry|Goldreich-19b|Oded Goldreich. ''On the complexity of estimating the effective support size.'' Electronic Colloquium on Computational Complexity (ECCC), 26:88, 2019.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GoldreichGR-98|Oded Goldreich, Shafi Goldwasser, and Dana Ron. ''Property testing and its connection to learning and approximation.'' J. ACM, 45(4):653–750, 1998.}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Open Problems:98

2019-08-07T21:35:39Z

Ccanonne:

{{Header
|title=Estimating a Graph's Degree Distribution
|source=wola19
|who=C. Seshadhri
}}
The ''degree distribution'' of a graph $G=(V,E)$ is the histogram of the degree frequencies: i.e., letting $n(d)$ denote the number of degree-$d$ vertices, the histogram $(n(d))_{d\geq 0}$. Define the (complementary) cumulative distribution function as
\[
N(d) \stackrel{\rm def}{=} \sum_{d'\geq d} n(d'), \qquad d\geq 0\,.
\]
Assume one has access to the graph $G$ via the following (standard) three types of queries:

- sampling a u.a.r. vertex

- querying the degree of a given vertex

- sample a u.a.r. neighbor of a given vertex

and the goal is to obtain the following $(1\pm \varepsilon)$-"bicriteria" approximation $\hat{N}$ of the degree distribution: for all $d$,
\[
(1-\varepsilon)N( (1-\varepsilon)d) \leq \hat{N}(d) \leq (1+\varepsilon) N((1+\varepsilon)d)\,.
\]
Previous work of Eden, Jain, Pinar, Ron, and Seshadhri {{Cite|EdenJPRS-18}} shows an upper bound of
\[
\frac{n}{h} + \frac{m}{\min_d d\cdot N(d)}
\]
queries, where $h$ is the value s.t. $N(h)=h$ (where the complementary cdf intersects the diagonal).

'''Question:''' Can this upper bound be improved? Can one establish matching lower bounds?

And also, slightly less well-defined:

'''Question:''' Can one obtain better upper bounds when relaxing the goal to only learn the ''high-degree'' (tail) part of the distribution? What about testing properties of the degree distribution (e.g., "power-law-ness") in this setting? And what about the first type of queries — can one relax it, or work with a different type of sampling than uniform (for instance, via random walks)?

Open Problems:99

2019-08-07T21:35:07Z

Ccanonne:

{{Header
|title=Vertex-Distribution-Free Graph Testing
|source=wola19
|who=Oded Goldreich
}}
The graph query model where one gets to query vertices uniformly at random may seem unrealistic in some cases. Thus, one may advocate alternative models, especially in the context of graph property testing, akin to the "distribution-free" model of property testing (for functions) and the PAC model (for learning). In this ''Vertex-Distribution-Free'' (VDF) model of testing suggested in a recent paper {{Cite|Goldreich-19a}} ''(note: this model was also briefly discussed in Section 10.1 of {{Cite|GoldreichGR-98}})'', one gets i.i.d. vertices sampled from an arbitrary distribution $\mathcal{D}$ over the vertex set, and the goal is to test w.r.t. to the (pseudo) distance induced by $\mathcal{D}$.

'''Question:''' Perform a systematic study of property testing, both in the bounded-degree and dense graph models, in this VDF setting.

'''Question:''' ''(Suggested by C. Seshadhri)'' Can one define, motivate, and prove non-trivial results in an ''Edge''-Distribution-Free model, analogous to the VDF one but with regard to sampling random edges? ''(Note: This type of variant was also briefly evoked in Section 10.1.4 of {{Cite|GoldreichGR-98}}, where it was shown that Bipartiteness is not testable in such an EDF model.)''

Open Problems:98

2019-08-07T21:30:53Z

Ccanonne:

{{Header
|title=Estimating a Graph's Degree Distribution
|source=wola19
|who=C. Seshadhri
}}
The ''degree distribution'' of a graph $G=(V,E)$ is the histogram of the degree frequencies: i.e., letting $n(d)$ denote the number of degree-$d$ vertices, the histogram $(n(d))_{d\geq 0}$. Define the (complementary) cumulative distribution function as
\[
N(d) \stackrel{\rm def}{=} \sum_{d'\geq d} n(d'), \qquad d\geq 0\,.
\]
Assume one has access to the graph $G$ via the following (standard) three types of queries:
- sampling a u.a.r. vertex
- querying the degree of a given vertex
- sample a u.a.r. neighbor of a given vertex
and the goal is to obtain the following $(1\pm \varepsilon)$-"bicriteria" approximation $\hat{N}$ of the degree distribution: for all $d$,
\[
(1-\varepsilon)N( (1-\varepsilon)d) \leq \hat{N}(d) \leq (1+\varepsilon) N((1+\varepsilon)d)\,.
\]
Previous work of Eden, Jain, Pinar, Ron, and Seshadhri {{Cite|EdenJPRS-18}} shows an upper bound of
\[
\frac{n}{h} + \frac{m}{\min_d d\cdot N(d)}
\]
queries, where $h$ is the value s.t. $N(h)=h$ (where the complementary cdf intersects the diagonal).

'''Question:''' Can this upper bound be improved? Can one establish matching lower bounds?

And also, slightly less well-defined:

'''Question:''' Can one obtain better upper bounds when relaxing the goal to only learn the ''high-degree'' (tail) part of the distribution? What about testing properties of the degree distribution (e.g., "power-law-ness") in this setting? And what about the first type of queries — can one relax it, or work with a different type of sampling than uniform (for instance, via random walks)?

Open Problems:99

2019-08-07T21:30:06Z

Ccanonne:

{{Header
|title=Vertex-Distribution-Free Graph Testing
|source=wola19
|who=Oded Goldreich
}}
The graph query model where one gets to query vertices uniformly at random may seem unrealistic in some cases. Thus, one may advocate alternative models, especially in the context of graph property testing, akin to the "distribution-free" model of property testing (for functions) and the PAC model (for learning). In this ''Vertex-Distribution-Free'' (VDF) model of testing suggested in a recent paper {{Cite|Goldreich-19}} ''(note: this model was also briefly discussed in Section 10.1 of {{Cite|GoldreichGR-98}})'', one gets i.i.d. vertices sampled from an arbitrary distribution $\mathcal{D}$ over the vertex set, and the goal is to test w.r.t. to the (pseudo) distance induced by $\mathcal{D}$.

'''Question:''' Perform a systematic study of property testing, both in the bounded-degree and dense graph models, in this VDF setting.

'''Question:''' ''(Suggested by C. Seshadhri)'' Can one define, motivate, and prove non-trivial results in an ''Edge''-Distribution-Free model, analogous to the VDF one but with regard to sampling random edges? ''(Note: This type of variant was also briefly evoked in Section 10.1.4 of {{Cite|GoldreichGR-98}}, where it was shown that Bipartiteness is not testable in such an EDF model.)''

Open Problems:99

2019-08-07T21:29:52Z

Ccanonne:

{{Header
|title=Vertex-Distribution-Free Graph Testing
|source=wola19
|who=Oded Goldreich
}}
The graph query model where one gets to query vertices uniformly at random may seem unrealistic in some cases. Thus, one may advocate alternative models, especially in the context of graph property testing, akin to the "distribution-free" model of property testing (for functions) and the PAC model (for learning). In this ''Vertex-Distribution-Free'' (VDF) model of testing suggested in a recent paper {{Cite|Goldreich-19}} ''(note: this model was also briefly discussed in Section 10.1 of {{Cite|GoldreichGR-98}})'', one gets i.i.d. vertices sampled from an arbitrary distribution $\mathcal{D}$ over the vertex set, and the goal is to test w.r.t. to the (pseudo) distance induced by $\mathcal{D}$.

'''Question:'''Perform a systematic study of property testing, both in the bounded-degree and dense graph models, in this VDF setting.

'''Question:''' ''(Suggested by C. Seshadhri)'' Can one define, motivate, and prove non-trivial results in an ''Edge''-Distribution-Free model, analogous to the VDF one but with regard to sampling random edges? ''(Note: This type of variant was also briefly evoked in Section 10.1.4 of {{Cite|GoldreichGR-98}}, where it was shown that Bipartiteness is not testable in such an EDF model.)''

Open Problems:99

2019-08-07T21:28:48Z

Ccanonne: Created page with "{{Header |title=Vertex-Distribution-Free Graph Testing |source=wola19 |who=Oded Goldreich }} The graph query model where one gets to query vertices uniformly at random, as men..."

{{Header
|title=Vertex-Distribution-Free Graph Testing
|source=wola19
|who=Oded Goldreich
}}
The graph query model where one gets to query vertices uniformly at random, as mentioned in the previous open problem, may seem unrealistic in some cases. Thus, one may advocate alternative models, especially in the context of graph property testing, akin to the "distribution-free" model of property testing (for functions) and the PAC model (for learning). In this ''Vertex-Distribution-Free'' (VDF) model of testing suggested in a recent paper {{Cite|Goldreich-19}} ''(note: this model was also briefly discussed in Section 10.1 of {{Cite|GoldreichGR-98}})'', one gets i.i.d. vertices sampled from an arbitrary distribution $\mathcal{D}$ over the vertex set, and the goal is to test w.r.t. to the (pseudo) distance induced by $\mathcal{D}$.

'''Question:'''Perform a systematic study of property testing, both in the bounded-degree and dense graph models, in this VDF setting.

'''Question:''' ''(Suggested by C. Seshadhri)'' Can one define, motivate, and prove non-trivial results in an ''Edge''-Distribution-Free model, analogous to the VDF one but with regard to sampling random edges? ''(Note: This type of variant was also briefly evoked in Section 10.1.4 of {{Cite|GoldreichGR-98}}, where it was shown that Bipartiteness is not testable in such an EDF model.)''

Bibliography

2019-08-07T21:28:37Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages 449–458. 2018.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-19|Oded Goldreich. ''Testing graphs in vertex-distribution-free models.'' In ''STOC'', pages 527–534, 2019.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GoldreichGR-98|Oded Goldreich, Shafi Goldwasser, and Dana Ron. ''Property testing and its connection to learning and approximation.'' J. ACM, 45(4):653–750, 1998.}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Bibliography

2019-08-07T21:27:14Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages 449–458. 2018.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GoldreichGR-98|Oded Goldreich, Shafi Goldwasser, and Dana Ron. ''Property testing and its connection to learning and approximation.'' J. ACM, 45(4):653–750, 1998.}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Bibliography

2019-08-07T21:20:56Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages 449–458. 2018.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Bibliography

2019-08-07T21:20:25Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|EdenJPRS-18|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages
449–458. 2018..}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Bibliography

2019-08-07T21:19:50Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. ''Provable and practical approximations for the degree distribution using sublinear graph samples.'' In ''WWW'', pages
449–458. 2018..}}

{{bibentry|EdenJPRS-18|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Open Problems:98

2019-08-07T21:18:01Z

Ccanonne: Created page with "{{Header |title=Estimating a Graph's Degree Distribution |source=wola19 |who=C. Seshadhri }} The ''degree distribution'' of a graph $G=(V,E)$ is the histogram of the degree fr..."

{{Header
|title=Estimating a Graph's Degree Distribution
|source=wola19
|who=C. Seshadhri
}}
The ''degree distribution'' of a graph $G=(V,E)$ is the histogram of the degree frequencies: i.e., letting $n(d)$ denote the number of degree-$d$ vertices, the histogram $(n(d))_{d\geq 0}$. Define the (complementary) cumulative distribution function as
\[
N(d) \eqdef \sum_{d'\geq d} n(d'), \qquad d\geq 0\,.
\]
Assume one has access to the graph $G$ via the following (standard) three types of queries:
- sampling a u.a.r. vertex
- querying the degree of a given vertex
- sample a u.a.r. neighbor of a given vertex
and the goal is to obtain the following $(1\pm \varepsilon)$-"bicriteria" approximation $\hat{N}$ of the degree distribution: for all $d$,
\[
(1-\varepsilon)N( (1-\varepsilon)d) \leq \hat{N}(d) \leq (1+\varepsilon) N((1+\varepsilon)d)\,.
\]
Previous work of Eden, Jain, Pinar, Ron, and Seshadhri {{Cite|EdenJPRS-18}} shows an upper bound of
\[
\frac{n}{h} + \frac{m}{\min_d d\cdot N(d)}
\]
queries, where $h$ is the value s.t. $N(h)=h$ (where the complementary cdf intersects the diagonal).

'''Question:''' Can this upper bound be improved? Can one establish matching lower bounds?

And also, slightly less well-defined:

'''Question:''' Can one obtain better upper bounds when relaxing the goal to only learn the ''high-degree'' (tail) part of the distribution? What about testing properties of the degree distribution (e.g., "power-law-ness") in this setting? And what about the first type of queries — can one relax it, or work with a different type of sampling than uniform (for instance, via random walks)?

Open Problems:97

2019-08-07T21:14:37Z

Ccanonne: Created page with "{{Header |title=Local Computation Algorithm for MIS |source=wola19 |who=Mohsen Gaffhari }} In the model of Local Computation Algorithms (LCA), given an input graph $G=(V,E)$,..."

{{Header
|title=Local Computation Algorithm for MIS
|source=wola19
|who=Mohsen Gaffhari
}}

In the model of Local Computation Algorithms (LCA), given an input graph $G=(V,E)$, an algorithm gets, upon query any vertex $v$ of its choosing, the list of neighbors of $v$. In this model, the current state-of-the-art for the query complexity of computing a Maximal Independent Set (MIS) for graph $G$ of maximum degree at most $\Delta$ is an upper bound of
$$
\Delta^{O(\log\log \Delta)} \operatorname{poly}\!\log n
$$
queries.

'''Question:''' Does there exist a $\operatorname{poly}(\log n, \Delta)$-query LCA for MIS?

Open Problems:96

2019-08-07T20:38:31Z

Ccanonne:

{{Header
|title=Identity Testing Up to Coarsenings
|source=wola19
|who=Clément Canonne
}}
Given a distance parameter $\varepsilon\in(0,1]$, i.i.d. samples from an unknown distribution $p$ and a (known) reference distribution $q$, both over $[n] = \{1,\dots,n\}$, the identity testing question asks for the minimum number of samples sufficient to distinguish, with probability at least $2/3$, between (i) $p=q$ and (ii) $\operatorname{d}_{\rm TV}(p,q) > \varepsilon$. ($\operatorname{d}_{\rm TV}$ here denotes the total variation distance.) This question is by now fully resolved, with $\Theta(\sqrt{n}/\varepsilon^2)$ samples being necessary and sufficient {{Cite|Paninski-08|ValiantV-14}}.

However, consider the following variant: given a (fixed) family $\mathcal{F}$ of functions from $[n]$ to $[m]$, and a reference distribution $q$ over $[m]$, distinguish between (i) there exists $f\in \mathcal{F}$, $p = q\circ f$, and (ii) $\min_{f\in\mathcal{F}} \operatorname{d}_{\rm TV}(p,q\circ f) > \varepsilon$.

This ''$\mathcal{F}$-identity testing'' question includes the identity testing one as special case by setting $m=n$ and $\mathcal{F}$ to be the singleton containing the identity function. One can also take $m=n$ and $\mathcal{F}$ to be the class of all permutations, to test "identity up to relabeling" (a problem whose sample complexity is, from previous work of Valiant and Valiant, known to be $\Theta(n/(\varepsilon^2\log n))$ (see Corollary 11.30 of {{Cite|Goldreich-17}}).

'''Question:''' For a fixed $m$, and $\mathcal{F}$ the family of all partitions of $[n]$ into $m$ consecutive intervals, what is the sample complexity of $\mathcal{F}$-identity testing, as a function of $n,\varepsilon,m$?

''Note: this corresponds to testing whether $p$ is a ``refinement'' of the coarse distribution $q$; or, equivalently, if $p$ ad $q$ are the same, up to the precision of the measurements.''

Open Problems:96

2019-08-07T20:36:36Z

Ccanonne: Created page with "Given a distance parameter $\varepsilon\in(0,1]$, i.i.d. samples from an unknown distribution $p$ and a (known) reference distribution $q$, both over $[n] = \{1,\dots,n\}$, th..."

Given a distance parameter $\varepsilon\in(0,1]$, i.i.d. samples from an unknown distribution $p$ and a (known) reference distribution $q$, both over $[n] = \{1,\dots,n\}$, the identity testing question asks for the minimum number of samples sufficient to distinguish, with probability at least $2/3$, between (i) $p=q$ and (ii) $\operatorname{d}_{\rm TV}(p,q) > \varepsilon$. ($\operatorname{d}_{\rm TV}$ here denotes the total variation distance.) This question is by now fully resolved, with $\Theta(\sqrt{n}/\varepsilon^2)$ samples being necessary and sufficient {{Cite|Paninski-08|ValiantV-14}}.

However, consider the following variant: given a (fixed) family $\mathcal{F}$ of functions from $[n]$ to $[m]$, and a reference distribution $q$ over $[m]$, distinguish between (i) there exists $f\in \mathcal{F}$, $p = q\circ f$, and (ii) $\min_{f\in\mathcal{F}} \operatorname{d}_{\rm TV}(p,q\circ f) > \varepsilon$.

This ''$\mathcal{F}$-identity testing'' question includes the identity testing one as special case by setting $m=n$ and $\mathcal{F}$ to be the singleton containing the identity function. One can also take $m=n$ and $\mathcal{F}$ to be the class of all permutations, to test "identity up to relabeling" (a problem whose sample complexity is, from previous work of Valiant and Valiant, known to be $\Theta(n/(\varepsilon^2\log n))$ (see Corollary 11.30 of {{Cite|Goldreich-17}}).

'''Question:''' For a fixed $m$, and $\mathcal{F}$ the family of all partitions of $[n]$ into $m$ consecutive intervals, what is the sample complexity of $\mathcal{F}$-identity testing, as a function of $n,\varepsilon,m$?

''Note: this corresponds to testing whether $p$ is a ``refinement'' of the coarse distribution $q$; or, equivalently, if $p$ ad $q$ are the same, up to the precision of the measurements.''

Bibliography

2019-08-07T20:36:18Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Bibliography

2019-08-07T20:35:51Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh. ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ''ICML'', 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi. ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|Alon-02|Noga Alon. ''Testing subgraphs in large graphs.'' Random Struct. Algorithms, 21(3-4):359-370, 2002.}}

{{bibentry|AlonFNS-09|Noga Alon, Eldar Fischer, Ilan Newman, and Asaf Shapira. ''A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity.'' SIAM J. Comput. 39(1):143-167, 2009.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatsonSS-14|Joshua D. Batson, Daniel A. Spielman, and Nikhil Srivastava. ''Twice-Ramanujan Sparsifiers.'' SIAM Review 56(2):315-334, 2014.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenczurK-96|András A. Benczúr and David R. Karger. ''Approximating $s{-}t$ minimum cuts in $\tilde O(n^2)$ time.'' In ''ACM Symposium on Theory of Computing'', pages 47-55, 1996.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|CarlsonKST-17|Charles Carlson, Alexandra Kolla, Nikhil Srivastava, and Luca Trevisan. ''Optimal Lower Bounds for Sketching Graph Cuts.'' In ''CoRR,'' abs/1712.10261, 2017.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24:155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' In ''SODA'', 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|Goldreich-17|Oded Goldreich. ''Introduction to Property Testing.'' Cambridge University Press, November 2017.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KamathT-19|Gautam Kamath, Christos Tzamos. ''Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing.'' In ''SODA'', 2019.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMSY-18|Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In CCC'18, https://eccc.weizmann.ac.il/report/2016/174/}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NewmanR-13|Ilan Newman and Yuri Rabinovich. ''On Multiplicative $\lambda$-Approximations and Some Geometric Applications.'' SIAM J. Comput. 42(3):855-883, 2013.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.'' PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|Paninski-08|Liam Paninski. ''A coincidence-based test for uniformity given very sparsely sampled discrete data.'' In ''IEEE Trans. Information Theory,'' 54(10):4750–4755, 2008.

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|Pogrow-17|Yosef Pogrow. ''Solving Symmetric Diagonally Dominant Linear Systems in Sublinear Time and Some Observations on Graph Sparsification.'' MSc thesis, Weizmann Institute of Science, 2017.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Open Problems:95

2019-08-07T20:26:34Z

Ccanonne: Created page with "{{Header |title=Non-Adaptive Group Testing |source=wola19 |who=Oliver Gebhard }} In (non-adaptive) quantitative group testing, one has a population of $n$ individuals, among w..."

{{Header
|title=Non-Adaptive Group Testing
|source=wola19
|who=Oliver Gebhard
}}
In (non-adaptive) quantitative group testing, one has a population of $n$ individuals, among which $k= n^c$ (for some constant $c\in(0,1)$) are sick. The goal is, by performing $m$ non-adaptive tests, to identity the $k$ sick individuals (where a test is a subset $S\subseteq [n]$, whose output is $1$ if $S$ contains at least one sick individual).

By a counting argument, one gets a lower bound of $m = \Omega\big( \frac{k}{\log k}\log \frac{n}{k} \big)$ tests; however, the best known upper bound is $m = O( k\log \frac{n}{k} )$.

'''Question:''' Can one get rid of the $\log k$ factor in the lower bound; or, conversely, improve the upper bound to match it?

Waiting

2019-08-07T20:15:11Z

Ccanonne:

{{DISPLAYTITLE:Waiting Room}}
Submitting a new problem:
# Make sure your problem is not yet on [[Open_Problems:By_Number|the list]].
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== Problems in Preparation ==

*[[Waiting:Sample Problem|Sample Problem]] ← Please do not remove or edit!

The Warwick workshop:

*[[Waiting:Dense_Graph_Property_Testing_Tradeoffs]]
*[[Waiting:Cut-Sparsification_of_Hypergraphs]]

WoLA'19:
*[[Waiting:Non-Adaptive Group Testing]]
*[[Waiting:Identity Testing Up to Coarsenings]]
*[[Waiting:Local Computation Algorithm for MIS]]
*[[Waiting:Estimating a Graph's Degree Distribution]]
*[[Waiting:Vertex-Distribution-Free Graph Testing]]
*[[Waiting:Effective Support Size Estimation in the Dual Model]]
*[[Waiting:Vertex connectivity in the LOCAL model]]
*[[Waiting:Making edges happy in the LOCAL model]]

Open Problems:90

2018-03-27T20:04:08Z

Ccanonne:

{{Header
|title=Dense Graph Property Testing "Tradeoffs"
|source=online
|who=Clement Canonne
}}

In the dense graph model of property testing (where the testing algorithm is granted query access to the adjacency matrix of an unknown $n$-node graph, and the distance measure is the fraction of entries of this matrix that needs to be changed for the graph to satisfy the property), ''testability'' was originally defined as meaning "a number of queries depending only on the proximity parameter $\varepsilon$ (but not $n$)".

Many properties, such as graph partition properties, triangle-freeness, and more generally $H$-freeness, are known to be testable with a constant number of queries (in the above sense). Moreover, we now have a full characterization of the graph properties which admit such $O_\varepsilon(1)$-query testers.

Yet, these results are typically obtained via regularity lemmata, such as Szemerédi's Regularity Lemma, and the "constant" query complexity if often superpolynomial in $1/\varepsilon$ (or, often, even a tower of exponent size $\operatorname{poly}(1/\varepsilon)$). This is not an oversight: triangle freeness, for instance, provably does '''not''' have any tester with query complexity $\operatorname{poly}(1/\varepsilon)$. (
See for instance Section 8.5 of Oded Goldreich's *Introduction to Property Testing* book for a summary of the state-of-the-art in property testing in the dense graph model.)

However, nothing ''a priori'' precludes these properties to have testers with query complexity $\sqrt{n}\operatorname{poly}(1/\varepsilon)$, $\operatorname{poly}(\log n, 1/\varepsilon)$, or even $\operatorname{poly}(\log^* n, 1/\varepsilon)$. What is the best possible tradeoff between $n$ and $\varepsilon$ one can achieve? (Note that ''every'' property trivially has a tester with query complexity $O(n^2)$, so it's only a question of how far down this dependence on $n$ can be brought while keeping a reasonable dependence on $\varepsilon$)

As a concrete instance of the problem:

'''Open problem.''' Is there a $\operatorname{poly}(\log n, 1/\varepsilon)$-query tester for triangle freeness in the dense graph model?

Open Problems:90

2018-03-27T20:03:42Z

Ccanonne: Created page with "{{Header |title=Dense Graph Property Testing "Tradeoffs" |source=online |who=Clement Canonne }} In the dense graph model of property testing (where the testing algorithm is g..."

{{Header
|title=Dense Graph Property Testing "Tradeoffs"
|source=online
|who=Clement Canonne
}}

In the dense graph model of property testing (where the testing algorithm is granted query access to the adjacency matrix of an unknown $n$-node graph, and the distance measure is the fraction of entries of this matrix that needs to be changed for the graph to satisfy the property), ''testability'' was originally defined as meaning "a number of queries depending only on the proximity parameter $\varepsilon$ (but not $n$)".

Many properties, such as graph partition properties, triangle-freeness, and more generally $H$-freeness, are known to be testable with a constant number of queries (in the above sense). Moreover, we now have a full characterization of the graph properties which admit such $O_\varepsilon(1)$-query testers.

Yet, these results are typically obtained via regularity lemmata, such as Szemerédi's Regularity Lemma, and the "constant" query complexity if often superpolynomial in $1/\varepsilon$ (or, often, even a tower of exponent size $\operatorname{poly}(1/\varepsilon)$). This is not an oversight: triangle freeness, for instance, provably does '''not''' have any tester with query complexity $\operatorname{poly}(1/\varepsilon)$. (
See for instance Section 8.5 of Oded Goldreich's *Introduction to Property Testing* book for a summary of the state-of-the-art in property testing in the dense graph model.)

However, nothing ''a priori'' precludes these properties to have testers with query complexity $\sqrt{n}\operatorname{poly}(\log n, 1/\varepsilon)$, $\operatorname{poly}(\log n, 1/\varepsilon)$, or even $\operatorname{poly}(\log^* n, 1/\varepsilon)$. What is the best possible tradeoff between $n$ and $\varepsilon$ one can achieve? (Note that ''every'' property trivially has a tester with query complexity $O(n^2)$, so it's only a question of how far down this dependence on $n$ can be brought while keeping a reasonable dependence on $\varepsilon$)

As a concrete instance of the problem:

'''Open problem.''' Is there a $\operatorname{poly}(\log n, 1/\varepsilon)$-query tester for triangle freeness in the dense graph model?

Waiting

2017-11-02T03:01:34Z

Ccanonne:

{{DISPLAYTITLE:Waiting Room}}
Submitting a new problem:
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== Problems in Preparation ==

*[[Waiting:Sample Problem|Sample Problem]] ← Please do not remove or edit!
* [[Waiting:Rényi entropy estimation|Rényi entropy estimation]]
* [[Waiting:Beyond identity testing|Beyond identity testing]]
* [[Waiting:Instance-optimal Hellinger testing|Instance-specific Hellinger testing]]
* [[Waiting:Efficient Pattern Maximum Likelihood Computation|Efficient Profile Maximum Likelihood Computation]]
* [[Waiting:Sample Stretching|Sample Stretching]]
* [[Waiting:Equivalence testing lower bound via communication complexity|Equivalence testing lower bound via communication complexity]]
* [[Waiting:Equivalence testing with conditional samples|Equivalence testing with conditional samples]]
* [[Waiting:Separating PDF and CDF query models|Separating PDF and CDF query models]]
* [[Waiting:Proofs of Proximity, AM vs. MA|Proofs of Proximity, AM vs. NP]]

Open Problems:87

2017-10-25T23:24:17Z

Ccanonne:

{{Header
|source=focs17
|who=Jayadev Acharya
|title=Equivalence testing with conditional samples
}}

''This is a continuation of [[Open_Problems:66|this previous open problem]] from the [[Workshops:Bertinoro_2014|Bertinoro]] workshop Bertinoro Workshop on Sublinear Algorithms.''

For constant $\varepsilon>0$ it is known that the sample complexity of equivalence testing, in the conditional oracle model where the algorithm gets to condition the samples it receives on arbitrary subsets of the domain $[n]$, is $\Omega(\sqrt{\log\log n})$ and $O({\log\log n})$. {{cite|AcharyaCK-14,FalahatgarJOPS-15}}.

What is the exact dependence on the domain size of the sample complexity of equivalence testing in the conditional oracle model?

Open Problems:87

2017-10-25T22:57:57Z

Ccanonne:

{{Header
|source=focs17
|who=Gautam Kamath
|title=Equivalence testing with conditional samples
}}

''This is a continuation of [[Open_Problems:66|this previous open problem]] from the [[Workshops:Bertinoro_2014|Bertinoro]] workshop Bertinoro Workshop on Sublinear Algorithms.''

For constant $\varepsilon>0$ it is known that the sample complexity of equivalence testing, in the conditional oracle model where the algorithm gets to condition the samples it receives on arbitrary subsets of the domain $[n]$, is $\Omega(\sqrt{\log\log n})$ and $O({\log\log n})$. {{cite|AcharyaCK-14,FalahatgarJOPS-15}}.

What is the exact dependence on the domain size of the sample complexity of equivalence testing in the conditional oracle model?

Open Problems:87

2017-10-25T22:57:18Z

Ccanonne: Created page with "{{Header |source=focs17 |who=Gautam Kamath |title=Equivalence testing with conditional samples }} ''This is a continuation of this previous open problem..."

{{Header
|source=focs17
|who=Gautam Kamath
|title=Equivalence testing with conditional samples
}}

''This is a continuation of [[Open_Problems:66|this previous open problem]] from the [[Workshops:Bertinoro_2014||Bertinoro]] workshop Bertinoro Workshop on Sublinear Algorithms.''

For constant $\varepsilon>0$ it is known that the sample complexity of equivalence testing, in the conditional oracle model where the algorithm gets to condition the samples it receives on arbitrary subsets of the domain $[n]$, is $\Omega(\sqrt{\log\log n})$ and $O({\log\log n})$. {{cite|AcharyaCK-14,FalahatgarJOPS-15}}.

What is the exact dependence on the domain size of the sample complexity of equivalence testing in the conditional oracle model?

Bibliography

2017-10-25T22:30:08Z

Ccanonne:

'''Citations:''' Write <tt>{{cite|</tt>''paper_id_1''<tt>|</tt>''paper_id_2''<tt>|</tt>…<tt>|</tt>''paper_id_k''<tt>}}</tt> to cite papers ''paper_id_1'', ''paper_id_2'', …, ''paper_id_k''. For instance, <tt>{{cite|AlonMS-99|BlumLR-93}}</tt> results in {{cite|AlonMS-99|BlumLR-93}}.
<hr class="dontprint">

{{bibentry|AaronsonW-09|Scott Aaronson and Avi Wigderson. ''Algebrization: A New Barrier in Complexity Theory.'' ACM Transactions on Computation Theory, 1(1), 2009.}}

{{bibentry|AcharyaCK-14|Jayadev Acharya, Clément Canonne, and Gautam Kamath. ''A Chasm Between Identity and Equivalence Testing with Conditional Queries.'' In ''CoRR,'' abs/1411.7346, 2014.}}

{{bibentry|AcharyaDOS-17|Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh . ''Estimating Symmetric Properties of Distributions: A Maximum Likelihood Approach .'' In ICML, 2017.}}

{{bibentry|AcharyaOST-17|Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi . ''Estimating Renyi Entropy of Discrete Distributions.'' In IEEE Transactions on Information Theory, vol. 63, no. 1, pages 38-56, 2017.}}

{{bibentry|AhnG-09|Kook Jin Ahn and Sudipto Guha. ''Graph sparsification in the semi-streaming model.'' In ''International Colloquium on Automata, Languages and Programming'', pages 328-338, 2009.}}

{{bibentry|AhnG-11|Kook Jin Ahn and Sudipto Guha. ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}}

{{bibentry|AhnGM-12|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Analyzing graph structure via linear measurements.'' In ''SODA'', pages 459-467, 2012.}}

{{bibentry|AhnGM-12b|Kook Jin Ahn, Sudipto Guha, and Andrew McGregor. ''Graph sketches: sparsification, spanners, and subgraphs.'' In ''PODS'', pages 5-14, 2012.}}

{{bibentry|AilonL-11|Nir Ailon and Edo Liberty. ''An almost optimal unrestricted fast Johnson-Lindenstrauss transform.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 185-191, 2011.}}

{{bibentry|AlonMS-99|Noga Alon, Yossi Matias, Mario Szegedy. ''The Space Complexity of Approximating the Frequency Moments.'' J. Comput. Syst. Sci. 58(1):137-147, 1999.}}

{{bibentry|AndoniCKQWZ-16| Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. ''On Sketching Quadratic Forms.'' In ''ITCS'', pages 311-319, 2016.}}

{{bibentry|AndoniDIW-09|Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David P. Woodruff. ''Efficient sketches for earth-mover distance, with applications.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 324-330, 2009.}}

{{bibentry|AndoniGK-14|Alexandr Andoni, Anupam Gupta, and Robert Krauthgamer. ''Towards $(1+\varepsilon)$-Approximate Flow Sparsifiers.'' In ''SODA'', pages 279-293, 2014.}}

{{bibentry|AndoniIK-08|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Earth mover distance over high-dimensional spaces.'' In ''SODA'', pages 343-352, 2008.}}

{{bibentry|AndoniIK-09|Alexandr Andoni, Piotr Indyk, and Robert Krauthgamer. ''Overcoming the $\ell_1$ non-embeddability barrier: algorithms for product metrics.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 865-874, 2009.}}

{{bibentry|AndoniJP-10|Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. ''Lower bounds for edit distance and product metrics via Poincaré-type inequalities.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 184-192, 2010.}}

{{bibentry|AndoniKR-14|Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn. ''Sketching and Embedding are Equivalent for Norms.'' In ''CoRR,'' abs/1411.2577, 2014.}}

{{bibentry|AndoniN-12|Alexandr Andoni and Huy L. Nguyen. ''Width of points in the streaming model.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 447-452, 2012.}}

{{bibentry|AndoniO-09|Alexandr Andoni and Krzysztof Onak. ''Approximating edit distance in near-linear time.'' In ''ACM Symposium on Theory of Computing'', pages 199-204, 2009.}}

{{bibentry|AssadiKLY-16|Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. ''Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model.'' In ''SODA'', pages 1345-1364, 2016.}}

{{bibentry|AssadiKL-17|Sepehr Assadi, Sanjeev Khanna, and Yang Li. ''On Estimating Maximum Matching Size in Graph Streams.'' In ''SODA'', pages 1723-1742, 2017.}}

{{bibentry|BahBC-14|Bubaccar Bah, Luca Baldassarre, and Volkan Cevher. ''Model-based Sketching and Recovery with Expanders.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', 2014.}}

{{bibentry|BaraniukCDH-10|Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. ''Model-based compressive sensing.'' IEEE Transactions on Information Theory, 56(4):1982-2001, 2010.}}

{{bibentry|BarYossefJKS-04|Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''An information statistics approach to data stream and communication complexity.'' J. Comput. Syst. Sci., 68(4):702-732, 2004.}}

{{bibentry|BarYossefJKST-02|Ziv Bar-Yossef, T.S. Jayram, Ravi Kumar, D. Sivakumar, and Luca Trevisan. ''Counting distinct elements in a data stream.'' In ''Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science'', pages 1-10, 2002.}}

{{bibentry|BarYossefKS-02|Ziv Bar-Yossef, Ravi Kumar, and D. Sivakumar. ''Reductions in streaming algorithms, with an application to counting triangles in graphs.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 623-632, 2002.}}

{{bibentry|Baswana-06|Surender Baswana. ''Faster streaming algorithms for graph spanners.'' 2006.}}

{{bibentry|BatuFFKRW-01|Tugkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White. ''Testing random variables for independence and identity.'' In ''FOCS'', pages 442-451, 2001.}}

{{bibentry|BenderR-02|Michael A. Bender and Dana Ron. ''Testing properties of directed graphs: acyclicity and connectivity.'' Random Struct. Algorithms, 20(2):184-205, 2002.}}

{{bibentry|BenjaminiSS-08|Itai Benjamini, Oded Schramm, and Asaf Shapira. ''Every minor-closed property of sparse graphs is testable.'' In ''ACM Symposium on Theory of Computing'', pages 393-402, 2008.}}

{{bibentry|BenSassonGMSS-11|Eli Ben-Sasson, Elena Grigorescu, Ghid Maatouk, Amir Shpilka, and Madhu Sudan. ''On sums of locally testable affine invariant properties.'' Electronic Colloquium on Computational Complexity (ECCC), 18:79, 2011.}}

{{bibentry|BerindeIR-08|Radu Berinde, Piotr Indyk, and Milan Ruzic. ''Practical near-optimal sparse recovery in the $l_1$ norm.'' Allerton, 2008.}}

{{bibentry|BermanRY-14|Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev. ''$L_p$-Testing.'' In ''ACM Symposium on Theory of Computing'', pages 164-173, 2014.}}

{{bibentry|BhattacharyyaMMY-07|S. Bhattacharyya, A. Madeira, S. Muthukrishnan, and T. Ye. ''How to scalably skip past streams.'' In ''WSSP (Workshop with ICDE)'', 2007.}}

{{bibentry|BhuvanagiriG-06|Lakshminath Bhuvanagiri and Sumit Ganguly. ''Estimating entropy over data streams.'' In ''ESA'', pages 148-159, 2006.}}

{{bibentry|BhuvanagiriGKS-06|Lakshminath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha. ''Simpler algorithm for estimating frequency moments of data streams.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 708-713, 2006.}}

{{bibentry|BlaisCG-17| Eric Blais, Clément L. Canonne, and Tom Gur. ''Distribution Testing Lower Bounds via Reductions from Communication Complexity''. In ''CCC'', 2017.}}

{{bibentry|BlumLR-93|Manuel Blum, Michael Luby, and Ronitt Rubinfeld. ''Self-Testing/Correcting with Applications to Numerical Problems.'' J. Comput. Syst. Sci. 47(3):549-595, 1993.}}

{{bibentry|BogdanovOT-02|Andrej Bogdanov, Kenji Obata, and Luca Trevisan. ''A lower bound for testing 3-colorability in bounded-degree graphs.'' In ''FOCS'', pages 93-102, 2002.}}

{{bibentry|BonisGV-05|Annalisa De Bonis, Leszek Gasieniec, and Ugo Vaccaro. ''Optimal two-stage algorithms for group testing problems.'' SIAM J. Comput., 34(5):1253-1270, 2005.}}

{{bibentry|BoulandCHTV-16|Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, and Prashant Nalini Vasudevan. ''On SZK and PP.'' CoRR abs/1609.02888, 2016.}}

{{bibentry|BravermanGPW-13|Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. ''Information lower bounds via self-reducibility.'' In ''CSR'', 2013.}}

{{bibentry|BravermanO-10|Vladimir Braverman and Rafail Ostrovsky. ''Zero-one frequency laws.'' In ''ACM Symposium on Theory of Computing'', pages 281-290, 2010.}}

{{bibentry|BroderCFM-00|Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. ''Min-wise independent permutations.'' ''J. Comput. Syst. Sci.'', 60(3):630-659, 2000.}}

{{bibentry|BrodyC-09|Joshua Brody and Amit Chakrabarti. ''A multi-round communication lower bound for Gap Hamming and some consequences.'' In ''IEEE Conference on Computational Complexity'', pages 358-368, 2009.}}

{{bibentry|BrodyCRVW-10|Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, and Ronald de Wolf. ''Better Gap-Hamming lower bounds via better round elimination.'' In ''APPROX-RANDOM'', pages 476-489, 2010.}}

{{bibentry|BrodyJSW-14| Joshua Brody, Sune K. Jakobsen, Dominik Scheder, and Peter Winkler. ''Cryptogenography.'' In ''ITCS'', pages 13-22, 2014.}}

{{bibentry|BuriolFLMS-06|Luciana S. Buriol, Gereon Frahling, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Christian Sohler. ''Counting triangles in data streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 253-262, 2006.}}

{{bibentry|CandesRT-06|Emmanuel J. Candès, Justin K. Romberg, and Terence Tao. ''Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.'' IEEE Transactions on Information Theory, 52(1):489-509, 2006.}}

{{bibentry|CandesRT-06a|Emmanuel J. Candès, Justin Romberg, and Terence Tao. ''Stable signal recovery from incomplete and inaccurate measurements.'' Comm. Pure Appl. Math., 59(8):1208-1223, 2006.}}

{{bibentry|Canonne-15|Clément L. Canonne. ''Big Data on the rise? Testing monotonicity of distributions.'' In ''ICALP'', 2015.}}

{{bibentry|CanonneGR-16|Clément L. Canonne, Themis Gouleakis, and Ronitt Rubinfeld. ''Sampling Correctors.'' In ''ITCS'', 2016.}}

{{bibentry|CanonneRS-14|Clément L. Canonne, Dana Ron, and Rocco A. Servedio. ''Testing equivalence between distributions using conditional samples.'' In ''SODA'', pages 1174-1192, 2014.}}

{{bibentry|Chakrabarti-10|Amit Chakrabarti. ''A note on randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}}

{{bibentry|ChakrabartiCKM-10|Amit Chakrabarti, Graham Cormode, Ranganath Kondapally, and Andrew McGregor. ''Information cost tradeoffs for augmented index and streaming language recognition.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 387-396, 2010.}}

{{bibentry|ChakrabartiCM-07|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''A near-optimal algorithm for computing the entropy of a stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 328-335, 2007.}}

{{bibentry|ChakrabartiCM-09|Amit Chakrabarti, Graham Cormode, and Andrew McGregor. ''Annotations in data streams.'' In ''International Colloquium on Automata, Languages and Programming'', pages 222-234, 2009.}}

{{bibentry|ChakrabartiCMTV-15|Amit Chakrabarti, Graham Cormode, Andrew McGregor, Justin Thaler, and Suresh Venkatasubramanian. ''Verifiable Stream Computation and Arthur-Merlin Communication.'' In ''IEEE Conference on Computational Complexity'', pages 217-243, 2015.}}

{{bibentry|ChakrabartiK-14|Amit Chakrabarti and Sagar Kale. ''Submodular Maximization Meets Streaming: Matchings, Matroids, and More.'' In ''IPCO'', to appear, 2014.}}

{{bibentry|ChakrabartiR-11|Amit Chakrabarti and Oded Regev. ''An optimal lower bound on the communication complexity of Gap-Hamming-Distance.'' In ''ACM Symposium on Theory of Computing'', pages 51-60, 2011.}}

{{bibentry|ChakrabartiSWY-01|Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew C. Yao. ''Informational complexity and the direct sum problem for simultaneous message complexity.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 270-278, 2001.}}

{{bibentry|ChakrabartyS-13|Deeparnab Chakrabarty and C. Seshadhri. ''Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids.'' In ''ACM Symposium on Theory of Computing'', 2013.}}

{{bibentry|ChakrabortyFGM-13|Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah. ''On the power of conditional samples in distribution testing.'' In ''ITCS'', pages 561-580, 2013.}}

{{bibentry|ChanC-07|Timothy M. Chan and Eric Y. Chen. ''Multi-pass geometric algorithms.'' Discrete & Computational Geometry, 37(1):79-102, 2007.}}

{{bibentry|Charikar-02|Moses Charikar. ''Similarity estimation techniques from rounding algorithms.'' In ''STOC'', pages 380-388, 2002.}}

{{bibentry|ChazelleRT-05|Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. ''Approximating the Minimum Spanning Tree Weight in Sublinear Time.'' SIAM J. Comput. 34(6):1370-1379, 2005.}}

{{bibentry|ChienRS-03|Steve Chien, Lars Eilstrup Rasmussen, and Alistair Sinclair. ''Clifford algebras and approximating the permanent.'' J. Comput. Syst. Sci. 67(2), 2003.}}

{{bibentry|ChiesaG-17|Alessandro Chiesa and Tom Gur. ''Proofs of Proximity for Distribution Testing.'' Electronic Colloquium on Computational Complexity (ECCC) 24: 155, 2017.}}

{{bibentry|ChitnisCEHMMV-16|Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. ''Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams.'' In ''SODA'', pages 1326-1344, 2016.}}

{{bibentry|CormodeDIM-03|Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. ''Comparing data streams using hamming norms (how to zero in).'' ''IEEE Trans. Knowl. Data Eng.'', 15(3):529-540, 2003.}}

{{bibentry|CormodeKMS-06|Graham Cormode, Flip Korn, S. Muthukrishnan, and Divesh Srivastava. ''Space- and time-efficient deterministic algorithms for biased quantiles over data streams.'' In ''PODS'', pages 263-272, 2006.}}

{{bibentry|CormodeM-05|Graham Cormode and S. Muthukrishnan. ''An improved data stream summary: the count-min sketch and its applications.'' ''J. Algorithms'', 55(1):58-75, 2005.}}

{{bibentry|CormodeM-05a|Graham Cormode and S. Muthukrishnan. ''What's new: finding significant differences in network data streams.'' ''IEEE/ACM Trans. Netw.'', 13(6):1219-1232, 2005.}}

{{bibentry|CormodeM-05b|Graham Cormode and S. Muthukrishnan. ''Space efficient mining of multigraph streams.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 271-282, 2005.}}

{{bibentry|CormodeM-06|Graham Cormode and S. Muthukrishnan. ''Combinatorial algorithms for compressed sensing.''In Paola Flocchini and Leszek Gasieniec, editors, ''Structural Information and Communication Complexity, 13th International Colloquium, SIROCCO 2006, Chester, UK, July 2-5, 2006, Proceedings'', volume 4056 of ''Lecture Notes in Computer Science'', pages 280-294. Springer, 2006.}}

{{bibentry|CormodePSV-00|Graham Cormode, Mike Paterson, Suleyman Cenk Sahinalp, and Uzi Vishkin. ''Communication complexity of document exchange.'' In ''SODA'', 2000.}}

{{bibentry|CrouchM-11|Michael S. Crouch and Andrew McGregor. ''Periodicity and Cyclic Shifts via Linear Sketches.'' In ''APPROX'', 2011.}}

{{bibentry|CrouchS-14|Michael Crouch and Daniel Stubbs. In Andrew McGregor's presentation at the 2014 Bertinoro Workshop on Sublinear Algorithms.}}

{{bibentry|CzumajS-09|Artur Czumaj and Christian Sohler. ''Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time.'' In ''SIAM J. Comput.'', 39(3):904–922, 2009.}}

{{bibentry|DaskalakisDS-11|Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. ''Learning transformed product distributions.'' CoRR, abs/1103.0598, 2011.}}

{{bibentry|DaskalakisKW-18|Constantinos Daskalakis, Gautam Kamath, and John Wright. ''Which Distribution Distances are Sublinearly Testable?'' SODA, 2018.}}

{{bibentry|DasSarmaGP-08|Atish Das Sarma, Sreenivas Gollapudi, and Rina Panigrahy. ''Estimating PageRank on graph streams.'' In ''PODS'', pages 69-78, 2008.}}

{{bibentry|DeanG-04|Jeffrey Dean and Sanjay Ghemawat. ''MapReduce: Simplified data processing on large clusters.'' In ''OSDI'', pages 137-150, 2004.}}

{{bibentry|DemaineLM-02|Erik D. Demaine, Alejandro López-Ortiz, and J. Ian Munro. ''Frequency estimation of internet packet streams with limited space.'' In ''ESA'', pages 348-360, 2002.}}

{{bibentry|DemetrescuFR-06|Camil Demetrescu, Irene Finocchi, and Andrea Ribichini. ''Trading off space for passes in graph streaming problems.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 714-723, 2006.}}

{{bibentry|DodisGLRRS-99|Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, and Alex Samorodnitsky. ''Improved testing algorithms for monotonicity.'' In ''RANDOM-APPROX'', pages 97-108, 1999.}}

{{bibentry|DoerrK-16|Benjamin Doerr, Marvin Kunnemann. ''Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem.'' In ''ICALP'', 2016.}}

{{bibentry|Donoho-06|David L. Donoho. ''Compressed sensing.'' IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.}}

{{bibentry|DrakeH-03|Doratha E. Drake and Stefan Hougardy. ''Improved linear time approximation algorithms for weighted matchings.'' In ''RANDOM-APPROX'', pages 14-23, 2003.}}

{{bibentry|DrineasMM-06|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Sampling algorithms for $\ell_2$ regression and applications.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1127-1136, 2006.}}

{{bibentry|DrineasMM-06a|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-based methods.'' In ''APPROX-RANDOM'', pages 316-326, 2006.}}

{{bibentry|DrineasMM-06b|Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan. ''Subspace sampling and relative-error matrix approximation: Column-row-based methods.'' In ''ESA'', pages 304-314, 2006.}}

{{bibentry|Eddy-04|Sean R Eddy. ''How do RNA folding algorithms work?'' Nature Biotechnology, 22, pages 1457-1458, 2004.}}

{{bibentry|Edmonds-65|Jack Edmonds. ''Maximum matching and a polyhedron with 0,1-vertices.'' J. Res. Nat. Bur. Standards, 69(B):125-130, 1965.}}

{{bibentry|Elkin-06|Michael Elkin. ''A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners.'' 2006.}}

{{bibentry|ElkinZ-06|Michael Elkin and Jian Zhang. ''Efficient algorithms for constructing $(1+\epsilon, \beta)$-spanners in the distributed and streaming models.'' Distributed Computing, 18(5):375-385, 2006.}}

{{bibentry|EpsteinLMS-11|Leah Epstein, Asaf Levin, Julian Mestre, and Danny Segev. ''Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model.'' SIAM J. Discrete Math. 25(3), 2011.}}

{{bibentry|ErgunJ-08|Funda Ergün and Hossein Jowhari. ''On distance to monotonicity and longest increasing subsequence of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 730-736, 2008.}}

{{bibentry|FalahatgarJOPS-15|Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapathi, and Ananda Theertha Suresh. ''Faster Algorithms for Testing under Conditional Sampling.'' In ''CoRR,'' abs/1504.04103, 2015.}}

{{bibentry|FeigenbaumKMSZ-05|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the streaming model: the value of space.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 745-754, 2005.}}

{{bibentry|FeigenbaumKMSZ-05a|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''On graph problems in a semi-streaming model.'' Theoretical Computer Science, 348(2-3):207-216, 2005.}}

{{bibentry|FeigenbaumKMSZ-08|Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. ''Graph distances in the data-stream model.'' SIAM J. Comput., 38(5):1709-1727, 2008.}}

{{bibentry|FeigenbaumKSV-02|Joan Feigenbaum, Sampath Kannan, Martin Strauss, and Mahesh Viswanathan. ''An approximate $L^1$ difference algorithm for massive data streams.'' ''Journal on Computing'', 32(1):131-151, 2002.}}

{{bibentry|FeldmanMSSS-06|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Cliff Stein, and Zoya Svitkina. ''On the complexity of processing massive, unordered, distributed data.'' 2006.}}

{{bibentry|FeldmanMSSS-10|Jon Feldman, S. Muthukrishnan, Anastasios Sidiropoulos, Clifford Stein, and Zoya Svitkina. ''On distributing symmetric streaming computations.'' ACM Transactions on Algorithms, 6(4), 2010.}}

{{bibentry|FichtenbergerPS-15|Hendrik Fichtenberger, Pan Peng, and Christian Sohler. ''On constant-size graphs that preserve the local structure of high-girth graphs.'' In ''APPROX-RANDOM,'' pages 786-799, 2015.}}

{{bibentry|Forster-01|Jurgen Forster. ''A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity.'' In ''IEEE Conference on Computational Complexity'', pages 100-106, 2001.}}

{{bibentry|GabizonH-10|Ariel Gabizon and Avinatan Hassidim. ''Derandomizing algorithms on product distributions and other applications of order-based extraction.'' In ''ICS'', pages 397-405, 2010.}}

{{bibentry|Gabow-90|Harold N. Gabow. ''Data structures for weighted matching and nearest common ancestors with linking.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 434-443, 1990.}}

{{bibentry|GalG-07|Anna Gál and Parikshit Gopalan. ''Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 294-304, 2007.}}

{{bibentry|Ganguly-06|Sumit Ganguly and Anirban Majumder. ''CR-precis: A deterministic summary structure for update data streams.'' In ''ESCAPE'', 2007.}}

{{bibentry|GilbertKMS-02|Anna C. Gilbert, Yannis Kotidis, S. Muthukrishnan, and Martin Strauss. ''How to summarize the universe: Dynamic maintenance of quantiles.'' In ''Proc. 28th International Conference on Very Large Data Bases'', pages 454-465, 2002.}}

{{bibentry|GilbertSTV-07|A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin. ''One sketch for all: fast algorithms for compressed sensing.'' ACM Symposium on Theory of Computing, 2007.}}

{{bibentry|GoldreichR-02|Oded Goldreich and Dana Ron. ''Property Testing in Bounded Degree Graphs.'' Algorithmica, 32(2):302-343, 2002}}

{{bibentry|GolubV-89|G.H. Golub and C.F. Van Loan. ''Matrix Computations.'' Johns Hopkins University Press, Baltimore, 1989.}}

{{bibentry|GomoryH-61|R. E. Gomory and T. C. Hu. ''Multi-terminal network flows.'' Journal of the Society for Industrial and Applied Mathematics, 9(4):551-570, 1961.}}

{{bibentry|GopalanJKK-07|Parikshit Gopalan, T. S. Jayram, Robert Krauthgamer, and Ravi Kumar. ''Estimating the sortedness of a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 318-327, 2007.}}

{{bibentry|GoreinovT-01|S. A. Goreinov and E. E. Tyrtyshnikov. ''The maximum-volume concept in approximation by low-rank matrices.'' Contemporary Mathematics, 280, pages 47-51, 2001.}}

{{bibentry|GoreinovTZ-97|S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. ''A theory of pseudoskeleton approximations.'' Linear Algebra and its Applications, 261, pages 1-21, August 1997.}}

{{bibentry|Gould-96|Stephen Jay Gould.''The Mismeasure of Man.'' W. W. Norton and Company, 1996.}}

{{bibentry|GreenwaldK-01|Michael Greenwald and Sanjeev Khanna. ''Space-efficient online computation of quantile summaries.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 58-66, 2001.}}

{{bibentry|GrigorescuKS-08|Elena Grigorescu, Tali Kaufman, and Madhu Sudan. ''2-transitivity is insufficient for local testability.'' In ''IEEE Conference on Computational Complexity'', pages 259-267, 2008.}}

{{bibentry|GroheGLSTV-07|Martin Grohe, Yuri Gurevich, Dirk Leinders, Nicole Schweikardt, Jerzy Tyszkiewicz, and Jan Van den Bussche. ''Database query processing using finite cursor machines.'' In ''ICDT'', pages 284-298, 2007.}}

{{bibentry|GuchtWWZ-15|Dirk Van Gucht, Ryan Williams, David P. Woodruff, and Qin Zhang. ''The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication.'' In ''PODS'', pages 199-212, 2015.}}

{{bibentry|GuE-96|M. Gu and S.C. Eisenstat. ''Efficient algorithms for computing a strong rank-revealing QR factorization.'' SIAM Journal on Scientific Computing, 17, pages 848-869, 1996.}}

{{bibentry|GuhaIM-07|Sudipto Guha, Piotr Indyk, and Andrew McGregor. ''Sketching information divergences.'' In ''Conference on Learning Theory'', 2007.}}

{{bibentry|GuhaM-06|Sudipto Guha and Andrew McGregor. ''Approximate quantiles and the order of the stream.'' In ''ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems'', pages 273-279, 2006.}}

{{bibentry|GuhaM-07|Sudipto Guha and Andrew McGregor. ''Lower bounds for quantile estimation in random-order and multi-pass streaming.'' Manuscript, 2007.}}

{{bibentry|GuhaM-07a|Sudipto Guha and Andrew McGregor. ''Space-efficient sampling.'' In ''AISTATS'', pages 169-176, 2007.}}

{{bibentry|GuhaM-08|Sudipto Guha and Andrew McGregor. ''Tight lower bounds for multi-pass stream computation via pass elimination.'' In ''International Colloquium on Automata, Languages and Programming'', pages 760-772, 2008.}}

{{bibentry|GuhaMV-06|Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian. ''Streaming and sublinear approximation of entropy and information distances.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 733-742, 2006.}}

{{bibentry|GuruswamiO-13|Venkatesan Guruswami and Krzysztof Onak. ''Superlinear lower bounds for multipass graph processing.'' In ''IEEE Conference on Computational Complexity'', 2013.}}

{{bibentry|GuruswamiR-05|Venkatesan Guruswami and Atri Rudra. ''Tolerant Locally Testable Codes.'' In ''Proceedings of the 9th International Workshop on Randomization and Computation (RANDOM)'', 2005.}}

{{bibentry|HagerupKNR-98|Torben Hagerup, Jyrki Katajainen, Naomi Nishimura, and Prabhakar Ragde. ''Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth.'' In J. Comput. Syst. Sci. (JCSS) 57(3):366-375, 1998.}}

{{bibentry|HarveyNO-08|Nicholas J. A. Harvey, Jelani Nelson, and Krzysztof Onak. ''Sketching and streaming entropy via approximation theory.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 489-498, 2008.}}

{{bibentry|HassidimKNO-09|Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguyen, and Krzysztof Onak. ''Local graph partitions for approximation and testing.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 22-31, 2009.}}

{{bibentry|HershbergerSST-04|John Hershberger, Nisheeth Shrivastava, Subhash Suri, and Csaba D. Tóth. ''Adaptive spatial partitioning for multidimensional data streams.'' In ''ISAAC'', pages 522-533, 2004.}}

{{bibentry|HoffmannMR-04|M. Hoffmann, S. Muthukrishnan, and R. Raman. ''Location streams: Models and algorithms.'' Technical Report 2004-28, DIMACS, May 2004.}}

{{bibentry|HopcroftK-73|John E. Hopcroft and Richard M. Karp. ''An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.'' SIAM J. Comput., 2(4):225-231, 1973.}}

{{bibentry|Indyk-00| Piotr Indyk. ''Stable distributions, pseudorandom generators, embeddings and data stream computation.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 189-197, 2000.}}

{{bibentry|Indyk-04| Piotr Indyk. ''Algorithms for dynamic geometric problems over data streams.'' In ''ACM Symposium on Theory of Computing'', pages 373-380, 2004.}}

{{bibentry|IndykP-11|Piotr Indyk and Eric Price. ''K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance.'' In ''ACM Symposium on Theory of Computing'', pages 627-636, 2011.}}

{{bibentry|IndykR-08|Piotr Indyk and Milan Ruzic. ''Near-optimal sparse recovery in the $\ell_1$ norm.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 199-207, 2008.}}

{{bibentry|IndykR-13|Piotr Indyk and Ilya Razenshteyn. ''On Model-Based RIP-1 Matrices.'' In ''International Colloquium on Automata, Languages and Programming (ICALP)'', pages 564-575, 2013.}}

{{bibentry|IndykT-03|Piotr Indyk and Niten Thaper. ''Fast color image retrieval via embeddings.'' Workshop on Statistical and Computational Theories of Vision (at ICCV), 2003.}}

{{bibentry|IndykW-03|Piotr Indyk and David P. Woodruff. ''Tight lower bounds for the distinct elements problem.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 283-288, 2003.}}

{{bibentry|IndykW-05|Piotr Indyk and David P. Woodruff. ''Optimal approximations of the frequency moments of data streams.'' In ''ACM Symposium on Theory of Computing'', pages 202-208, 2005.}}

{{bibentry|JainN-10|Rahul Jain and Ashwin Nayak. ''The space complexity of recognizing well-parenthesized expressions.'' Electronic Colloquium on Computational Complexity (ECCC), 17:71, 2010.}}

{{bibentry|Jakobsen-14|Sune Jakobsen. ''Information Theoretical Cryptogenography.'' In ''ITCS'', 2014.}}

{{bibentry|JayramKS-07|T. S. Jayram, Ravi Kumar, and D. Sivakumar. ''Simple lower bound on one-way Gap-Hamming.'' In http://www.cse.iitk.ac.in/users/sganguly/slides/ravikumar.pdf, 2007.}}

{{bibentry|JayramW-09|T. S. Jayram and David P. Woodruff. ''The data stream space complexity of cascaded norms.'' In ''IEEE Symposium on Foundations of Computer Science'', 2009.}}

{{bibentry|JhaR-11|Madhav Jha and Sofya Raskhodnikova. ''Testing and reconstruction of Lipschitz functions with applications to data privacy.'' Electronic Colloquium on Computational Complexity (ECCC), 18:57, 2011.}}

{{bibentry|Jowhari-12|Hossein Jowhari. ''Efficient Communication Protocols for Deciding Edit Distance.'' In ''ESA'', 2012.}}

{{bibentry|JowhariG-05|Hossein Jowhari and Mohammad Ghodsi. ''New streaming algorithms for counting triangles in graphs.'' In ''COCOON'', pages 710-716, 2005.}}

{{bibentry|KalantariS-95|Bahman Kalantari and Ali Shokoufandeh. ''Approximation schemes for maximum cardinality matching.'' Technical Report LCSR-TR-248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University, August 1995.}}

{{bibentry|KaneMSS-12|Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun. ''Counting Arbitrary Subgraphs in Data Streams.'' In ''Proceedings of the 39th International Colloquium on Automata, Languages, and Programming (2)'', 2012.}}

{{bibentry|KannanMY-16|Sampath Kannan, Elchanan Mossel, and Grigory Yaroslavtsev. ''Linear Sketching over $\mathbb{F}_2$.'' In ''CoRR,'' abs/1611.01879, 2016.}}

{{bibentry|Kapralov-12|Michael Kapralov. ''Improved lower bounds for matchings in the streaming model.'' In ''CoRR'', abs/1206.2269, 2012.}}

{{bibentry|KapralovKS-15|Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. ''Streaming Lower Bounds for Approximating MAX-CUT.'' In ''SODA'', pages 1263-1282, 2015.}}

{{bibentry|KapralovKSV-17|Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. ''$(1+\Omega(1))$-Approximation to MAX-CUT Requires Linear Space.'' In ''SODA'', pages 1703-1722, 2017.}}

{{bibentry|KarloffSV-10|Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. ''A model of computation for MapReduce.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 938-948, 2010.}}

{{bibentry|KerenidisLLRX-12|Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao. ''Lower bounds on information complexity via zero-communication protocols and applications.'' In ''FOCS'', 2012.}}

{{bibentry|KhanR-14|Arindam Khan and Prasad Raghavendra. ''On mimicking networks representing minimum terminal cuts.'' Inf. Process. Lett. (IPL) 114(7):365-371, 2014.}}

{{bibentry|KhotN-06|Subhash Khot and Assaf Naor. ''Nonembeddability theorems via Fourier analysis.'' Math. Ann., 334(4):821-852, 2006.}}

{{bibentry|KoganK-15|Dmitry Kogan and Robert Krauthgamer. ''Sketching Cuts in Graphs and Hypergraphs.'' In ''ITCS'', pages 367-376, 2015.}}

{{bibentry|KonradMM-12|Christian Konrad, Frederic Magniez, and Claire Mathieu. ''Maximum Matching in Semi-Streaming with Few Passes.'' In ''Proceedings of 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems,'' 2012.}}

{{bibentry|KrahmerW-11|Felix Krahmer, Rachel Ward. ''New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property.'' SIAM J. Math. Anal., 43(3):1269-1281, 2011.}}

{{bibentry|KuroseR-04|James F. Kurose and Keith W. Ross. ''Computer Networking: A Top-Down Approach Featuring the Internet.'' Addison Wesley, 2004.}}

{{bibentry|KushilevitzOR-00|Eyal Kushilevitz, Rafail Ostrovsky, and Yuval Rabani. ''Efficient search for approximate nearest neighbor in high dimensional spaces.'' SIAM J. Comput., 30(2):457-474, 2000.}}

{{bibentry|LarsenW-17|Kasper Green Larsen and Ryan Williams. ''Faster Online Matrix-Vector Multiplication.'' In ''SODA'', pages 2182-2189, 2017.}}

{{bibentry|LeviR-13|Reut Levi and Dana Ron. ''A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor.'' In ''CoRR'', abs/1302.3417, 2013.}}

{{bibentry|Li-06|Ping Li. ''Very sparse stable random projections, estimators and tail bounds for stable random projections.''}}

{{bibentry|LiHC-06|Ping Li, Trevor Hastie, and Kenneth Ward Church. ''Very sparse random projections.'' In ''KDD'', pages 287-296, 2006.}}

{{bibentry|LibenNowellVZ-06|David Liben-Nowell, Erik Vee, and An Zhu. ''Finding longest increasing and common subsequences in streaming data.'' J. Comb. Optim., 11(2):155-175, 2006.}}

{{bibentry|LibertySS-16|Edo Liberty, Ram Sriharsha, and Maxim Sviridenko. ''An Algorithm for Online K-Means Clustering.'' In ''ALENEX'', pages 81-89, 2016.}}

{{bibentry|MagniezMN-10|Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. ''Recognizing well-parenthesized expressions in the streaming model.'' In ''ACM Symposium on Theory of Computing'', pages 261-270, 2010.}}

{{bibentry|MahoneyMD-06|Michael W. Mahoney, Mauro Maggioni, and Petros Drineas. ''Tensor-cur decompositions for tensor-based data.'' In ''ACM SIGKDD international conference on knowledge discovery and data mining'', pages 327-336, 2006.}}

{{bibentry|ManjunathMPS-11|Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. ''Approximate Counting of Cycles in Streams.'' In ''Proceedings of the 19th Annual European Symposium'', 2011.}}

{{bibentry|MankuRL-98|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Approximate medians and other quantiles in one pass and with limited memory.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 426-435, 1998.}}

{{bibentry|MankuRL-99|Gurmeet Singh Manku, Sridhar Rajagopalan, and Bruce G. Lindsay. ''Random sampling techniques for space efficient online computation of order statistics of large datasets.'' In ''ACM SIGMOD International Conference on Management of Data'', pages 251-262, 1999.}}

{{bibentry|Matousek-02| Jiří Matoušek. ''Lectures on Discrete Geometry''. Springer, 2002.}}

{{bibentry|McGregor-05|Andrew McGregor. ''Finding graph matchings in data streams.'' In ''APPROX-RANDOM'', pages 170-181, 2005.}}

{{bibentry|McGregorRU-11|Andrew McGregor, Atri Rudra, and Steve Uurtamo. ''Polynomial Fitting of Data Streams with Applications to Codeword Testing.'' In ''Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)'', 2011.}}

{{bibentry|MetwallyAA-05|Ahmed Metwally, Divyakant Agrawal, and Amr El Abbadi. ''Efficient computation of frequent and top-k elements in data streams.'' In ''ICDT'', pages 398-412, 2005.}}

{{bibentry|MicaliV-80|Silvio Micali and Vijay V. Vazirani. ''An ${O}(\sqrt{V}{E})$ algorithm for finding maximum matching in general graphs.'' In ''FOCS'', pages 17-27, 1980.}}

{{bibentry|MisraG-82|Jayadev Misra and David Gries. ''Finding repeated elements.'' ''Sci. Comput. Program.'', 2(2):143-152, 1982.}}

{{bibentry|MitzenmacherV-08|Michael Mitzenmacher and Salil P. Vadhan. ''Why simple hash functions work: exploiting the entropy in a data stream.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 746-755, 2008.}}

{{bibentry|MontanaroO-09|Ashley Montanaro and Tobias Osborne. ''On the communication complexity of XOR functions.'' In ''CoRR,'' abs/0909.3392, 2009.}}

{{bibentry|MunroP-80|J. Ian Munro and Mike Paterson. ''Selection and sorting with limited storage.'' Theor. Comput. Sci., 12:315-323, 1980.}}

{{bibentry|Muthukrishnan-06|S. Muthukrishnan. ''Data streams: Algorithms and applications.'' Now Publishers, 2006.}}

{{bibentry|Muthukrishnan-06a|S. Muthukrishnan. ''Some algorithmic problems and results in compressed sensing.'' In ''Allerton Conference'', 2006.}}

{{bibentry|NaorS-06|Assaf Naor and Gideon Schechtman. ''Planar earthmover is not in $l_1$.'' In ''FOCS'', pages 655-666, 2006.}}

{{bibentry|NeedellT-10|Deanna Needell and Joel A. Tropp. ''Cosamp: iterative signal recovery from incomplete and inaccurate samples.'' Commun. ACM, 53(12):93-100, 2010.}}

{{bibentry|NguyenO-08|Huy N. Nguyen and Krzysztof Onak. ''Constant-time approximation algorithms via local improvements.'' In ''IEEE Symposium on Foundations of Computer Science'', pages 327-336, 2008.}}

{{bibentry|Onak-10|Krzysztof Onak. ''New Sublinear Methods in the Struggle Against Classical Problems.''PhD thesis, Massachusetts Institute of Technology, 2010.}}

{{bibentry|OnakRRR-12|Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld. ''A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 1123-1131, 2012.}}

{{bibentry|PettieS-04|Seth Pettie and Peter Sanders. ''A simpler linear time $2/3-\epsilon$ approximation for maximum weight matching.'' Inf. Process. Lett., 91(6):271-276, 2004.}}

{{bibentry|RudelsonV-06|Mark Rudelson and Roman Vershynin. ''Sparse reconstruction by convex relaxation: Fourier and gaussian measurements.'' In ''Proceedins of 40th Annual Conference on Information Sciences and Systems'', 2006.}}

{{bibentry|RudraU-10|Atri Rudra and Steve Uurtamo. ''Data Stream Algorithms for Codeword Testing.'' In ''Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP),'' 2010.}}

{{bibentry|SeshadhriV-11|C. Seshadhri and Jan Vondrák. ''Is submodularity testable?'' In ''ICS'', 2011.}}

{{bibentry|ShrivastavaBAS-04|Nisheeth Shrivastava, Chiranjeeb Buragohain, Divyakant Agrawal, and Subhash Suri. ''Medians and beyond: new aggregation techniques for sensor networks.'' In ''SenSys'', pages 239-249, 2004.}}

{{bibentry|Stewart-99|G.W. Stewart. ''Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix.'' Numerische Mathematik, 83, pages 313-323, 1999.}}

{{bibentry|Stewart-04|G.W. Stewart. ''Error analysis of the quasi-Gram-Schmidt algorithm.'' Technical Report UMIACS TR-2004-17 CMSC TR-4572, University of Maryland, College Park, MD, 2004.}}

{{bibentry|Thaler-16|Justin Thaler. ''Semi-Streaming Algorithms for Annotated Graph Streams.'' In ''ICALP'', 2016.}}

{{bibentry|Trevisan-09|Luca Trevisan. ''Max Cut and the smallest eigenvalue.'' In ''ACM Symposium on Theory of Computing'', pages 263-272, 2009.}}

{{bibentry|ValiantV-11|Gregory Valiant and Paul Valiant. ''The Power of Linear Estimators''. In ''FOCS'', 2011.}}

{{bibentry|ValiantV-14|Gregory Valiant and Paul Valiant. ''An Automatic Inequality Prover and Instance Optimal Identity Testing''. In ''FOCS'', 2014.}}

{{bibentry|Woodruff-04|David P. Woodruff. ''Optimal space lower bounds for all frequency moments.'' In ''ACM-SIAM Symposium on Discrete Algorithms'', pages 167-175, 2004.}}

{{bibentry|YoshidaYI-09|Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. ''An improved constant-time approximation algorithm for maximum matchings.'' In ''ACM Symposium on Theory of Computing'', pages 225-234, 2009.}}

Open Problems:88

2017-10-25T22:29:07Z

Ccanonne: Created page with "{{Header |source=focs17 |who=Clément Canonne |title=Separating PDF and CDF query models }} Recall that in the ''dual'' and ''cumulative dual'' models of distribution testing..."

{{Header
|source=focs17
|who=Clément Canonne
|title=Separating PDF and CDF query models
}}
Recall that in the ''dual'' and ''cumulative dual'' models of distribution testing {{cite|CanonneR-14}}, the testing is provided with two types of access to the unknown probability distribution $p$ (for the sake of the cumulative dual, over a totally ordered domain $[n]=\{1,\dots,n\}$): the first is the usual sampling oracle, which returns i.i.d. samples from $p$; and the second is an evaluation oracle, which on query $i\in[n]$ returns $p(i)$ (or, for the cumulative dual model, returns $p([1,i])=\sum_{j=1}^i p(j)$). In other words, the algorithm has sample access to $p$ ''and'' query access to its probability mass function (resp. cumulative distribution function).

It is immediate to see that the cumulative dual model is at least as powerful as the dual model, since any query to the pmf of $p$ can be simulated from 2 queries to its cdf. However, currently there is no strict separation known between dual and cumulative dual models for natural properties, i.e. a property $\mathcal{P}$ (or functional $\Phi$) of distributions for which testing (resp. estimation) requires asymptotically significantly more samples in the dual model than in the cumulative dual.

Does there exist such a separation?

Canonne and Rubinfeld show in {{cite|CanonneR-14}} a somewhat contrived separation, for estimating the entropy of distributions promised to be close to monotone. A natural conjecture would be that such a separation would exist for a property of functional where the total order (and thus the cumulative access) is essential, e.g. testing monotonicity or estimating distance to it. (The best currently known upper bounds for testing monotonicity are respectively $O((\log n)/\varepsilon)$ in the dual model, and $\tilde{O}(1/\varepsilon^4)$ in the cumulative dual {{cite|Canonne-15}}.)