Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The vertex separation number of a graph equals its path-width
Information Processing Letters
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Undirected connectivity in O(log/sup 1.5/n) space
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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We investigate the space complexity of the (undirected) graph accessibility problem (UGAP for short). We first observe that for a given graph G, the problem can be solved deterministically in space O(sw(G)2 log2 n), where n denotes the number of nodes and sw(G) denotes the separation-width of G that is an invariant of graphs introduced in this paper. We next observe that for the class of all graphs consisting of only two paths, the problem still remains to be hard for deterministic log-space under the NC1-reducibility. This result tells us that the problem is essentially hard for deterministic log-space.