S-T connectivity on digraphs with a known stationary distribution-Reference-Cited by-同舟云学术

S-T connectivity on digraphs with a known stationary distribution

Published:2011-07 Issue:3 Volume:7 Page:1-21
ISSN:1549-6325
Container-title:ACM Transactions on Algorithms
language:en
Short-container-title:ACM Trans. Algorithms

Author:

Chung Kai-Min¹,Reingold Omer²,Vadhan Salil¹

Affiliation:

1. Harvard University, Oxford, Cambridge, MA

2. Microsoft Research SVC, Mountain View, CA

Abstract

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 ).

Funder

Division of Computing and Communication Foundations

United States-Israel Binational Science Foundation

Office of Naval Research

Publisher

Association for Computing Machinery (ACM)

Subject

Mathematics (miscellaneous)

Link

https://dl.acm.org/doi/pdf/10.1145/1978782.1978785

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