S-T Connectivity on Digraphs with a Known Stationary Distribution

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 [15]. 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). ∗ ded abstract of this paper appeared in CCC 07 [4]. † Supported by NSF grant CCF-0133096. ‡ Supported by US-Israel BSF grant 2002246. § Supported by US-Israel BSF grant 2002246, NSF grant CCF-0133096, and ONR grant N00014-04-1-047. 1 

• Type: Conference
• Year: 2007
• Where: COCO
• Authors: Kai-Min Chung, Omer Reingold, Salil P. Vadhan
• Keywords: COCO 2007, Deterministic Logspace Algorithm, S-T Connectivity, US-Israel BSF Grant