A randomized time-space tradeoff of O/spl tilde/(mR/spl circ/) for USTCON

Authors:
U. Feige
Affiliations:
Dept. of Appl. Math., Weizmann Inst. of Sci., Rehovot, Israel
Venue:
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Year:
1993

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Voronoi-like nondeterministic partition of a lattice by collectives of finite automata

Mathematical and Computer Modelling: An International Journal

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Abstract

We present a randomized time space tradeoff of O/spl tilde/(mR/spl circ/) for undirected S-T-connectivity, where R/spl circ/ /spl Sigma//sub /spl upsi//spl epsiv/V/ 1/d/sub /spl upsi// is the virtual resistance of the graph. This solves an open question of Broder et al. (1989) (implicit also in Aleliunas et al. (1979)) who asked whether a tradeoff of O/spl tilde/(mn) is achievable, and also improves upon a tradeoff of O/spl tilde/(mn/d/sub min/) conjectured by Barnes and Feige (1993). Our algorithm is a modification of the Broder et al. algorithm. In passing, we also improve a result from Barnes and Feige regarding the rate at which a random walk discovers new vertices in a graph.