An O(log n log log n) space algorithm for undirected st-connectivity

Authors:
Vladimir Trifonov
Affiliations:
University of Texas at Austin, Austin, TX
Venue:
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Year:
2005

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Abstract

We present a deterministic O(log n log log n) space algorithm for undirected st-connectivity. It is based on the deterministic EREW algorithm of Chong and Lam [6] and uses the universal exploration sequences for trees constructed by Koucký [13]. Our result improves the O(log4/3 n) bound of Armoni et al.\ [2] and is a big step towards the optimal O(log n). Independently of our result and using a different set of techniques, the optimal bound was achieved by Reingold [18].