Difference between revisions of "Open Problems:22"

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|title=Random Walks
 
 
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Das Sarma et al. {{cite|DasSarmaGP-08}} simulate random walks to approximate the probability distribution on the vertices of the graph after a random walk of length $l$. What is the streaming complexity of approximating this distribution? What is the streaming complexity of finding the $k$ (approximately) most likely vertices after a walk of length $l$?
 
Das Sarma et al. {{cite|DasSarmaGP-08}} simulate random walks to approximate the probability distribution on the vertices of the graph after a random walk of length $l$. What is the streaming complexity of approximating this distribution? What is the streaming complexity of finding the $k$ (approximately) most likely vertices after a walk of length $l$?
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<b>Update</b>: See some progress in {{cite|ChenKPSSY21}}.

Latest revision as of 14:52, 23 July 2021

Suggested by Rina Panigrahy
Source Kanpur 2009
Short link https://sublinear.info/22

The paper of Das Sarma, Gollapudi, and Panigrahy [DasSarmaGP-08] shows a method for performing random walks in the streaming model. In particular, a random walk of length $l$ can be simulated using $O(n)$ space and $O(\sqrt{l})$ passes over the input stream. Is it possible to simulate such a random walk using $\tilde O(n)$ space and a much smaller number of passes, say, at most polylogarithmic in $n$ and $l$? The goal is either to show an algorithm or prove a lower bound.

Das Sarma et al. [DasSarmaGP-08] simulate random walks to approximate the probability distribution on the vertices of the graph after a random walk of length $l$. What is the streaming complexity of approximating this distribution? What is the streaming complexity of finding the $k$ (approximately) most likely vertices after a walk of length $l$?

Update: See some progress in [ChenKPSSY21].