Difference between revisions of "Open Problems:22"
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Revision as of 05:33, 8 November 2012
| Proposed by | Rina Panigrahy |
|---|---|
| Source | Kanpur 2009 |
| Short link | http://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 $l$?
