Difference between revisions of "Open Problems:47"

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'''Question:''' Can one achieve  $H = V = \tilde{O}(n)$?
'''Question:''' Can one achieve  $H = V = \tilde{O}(n)$?
== Update ==
This question was answered affirmatively by {{cite|Thaler-16}}.

Revision as of 15:45, 20 April 2017

Suggested by Graham Cormode
Source Bertinoro 2011
Short link https://sublinear.info/47

In the annotated stream model [ChakrabartiCM-09], a stream is augmented with ‘annotation’, which takes the form of a proof of a property of the stream. In its simplest form, the annotation may just be a reordering of the stream to make it easy to compute a function of interest. The key parameters in this model are $H$, the size of the annotation, and $V$, the space needed by the streaming party to view the stream and verify the proof. The annotation proposed should be such that an honest annotation will always be accepted, while a mistaken annotation will be detected and rejected with high probability.

We consider the problem of counting the number of triangles in a graph described by a stream of edges (where each edge is promised to occur at most once). Partial results from the above reference are that $H = O(n^2)$ and $V = \tilde{O}(1)$ is possible, as is $H = O(n^{3/2}), V= O(n^{3/2})$.

Question: Can one achieve $H = V = \tilde{O}(n)$?


This question was answered affirmatively by [Thaler-16].