S-T connectivity on digraphs with a known stationary distribution


Chung, Kai-Min, Omer Reingold, and Salil Vadhan. “S-T connectivity on digraphs with a known stationary distribution.” In ACM Transactions on Algorithms. Vol. 7. 3rd ed. ACM, 2011.
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Version history: Preliminary versions in CCC '07 and on ECCC (TR07-030).

We present a deterministic logspace algorithm for solving S-T Connectivity on directed graphs if: (i) we are given a stationary distribution of the random walk on the graph in which both of the input vertices \(s\) and \(t\) have nonnegligible probability mass and (ii) the random walk which starts at the source vertex \(s\) has polynomial mixing time. This result generalizes the recent deterministic logspace algorithm for S-T Connectivity on undirected graphs [Reingold, 2008]. It identifies knowledge of the stationary distribution as the gap between the S-T Connectivity problems we know how to solve in logspace (L) and those that capture all of randomized logspace (RL).


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Last updated on 07/15/2020