Randomized time-space tradeoffs for directed graph connectivity

Abstract

We present a spectrum of randomized time-space tradeoffs for solving directed graph connectivity or STCONN in small space. We use a strategy parameterized by a parameter k that uses k pebbles and performs short random walks of length n1/k using a probabilistic counter. We use this to get a family of algorithms that ranges between log2 n and log n in space and 2log2n and nn in running time. Our approach allows us to look at Savitch's algorithm and the random walk algorithm as two extremes of the same basic divide and conquer strategy. © Springer-Verlag Berlin Heidelberg 2003.