# Undirected connectivity in log-space

@article{Reingold2008UndirectedCI, title={Undirected connectivity in log-space}, author={Omer Reingold}, journal={J. ACM}, year={2008}, volume={55}, pages={17:1-17:24} }

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 log4/3(ṡ) 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…

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