Affiliation:
1. Weizmann Institute of Science Rehovot, Rehovot, Israel
Abstract
We present a
deterministic
, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log
4/3
(⋅) obtained by Armoni, Ta-Shma, Wigderson and Zhou (JACM 2000). As undirected st-connectivity is complete for the class of problems solvable by symmetric, nondeterministic, log-space computations (the class SL), this algorithm implies that SL = L (where L is the class of problems solvable by deterministic log-space computations). Independent of our work (and using different techniques), Trifonov (STOC 2005) has presented an
O
(log
n
log log
n
)-space, deterministic algorithm for undirected st-connectivity.
Our algorithm also implies a way to construct in log-space a
fixed
sequence of directions that guides a deterministic walk through all of the vertices of any connected graph. Specifically, we give log-space constructible universal-traversal sequences for graphs with restricted labeling and log-space constructible universal-exploration sequences for general graphs.
Funder
United States-Israel Binational Science Foundation
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
310 articles.
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