Simulating Random Walks on Graphs in the Streaming Model
Abstract
We study the problem of approximately simulating a $t$step random walk on a graph where the input edges come from a singlepass stream. The straightforward algorithm using reservoir sampling needs $O(nt)$ words of memory. We show that this space complexity is nearoptimal for directed graphs. For undirected graphs, we prove an $\Omega(n\sqrt{t})$bit space lower bound, and give a nearoptimal algorithm using $O(n\sqrt{t})$ words of space with $2^{\Omega(\sqrt{t})}$ simulation error (defined as the $\ell_1$distance between the output distribution of the simulation algorithm and the distribution of perfect random walks). We also discuss extending the algorithms to the turnstile model, where both insertion and deletion of edges can appear in the input stream.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.08205
 Bibcode:
 2018arXiv181108205J
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 To appear in ITCS 2019