2008/09/01 by Omer Reingold · 8 citations
Computer Science · #Complexity and Algorithms in Graphs #Advanced Graph Theory Research #Optimization and Search Problems
paper · doi:10.1145/1391289.1391291
openalex publication_date 2008/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/07
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.