A random NC algorithm for depth first search

Abstract

In this paper we present a fast parallel algorithm for constructing a depth first search tree for an undirected graph. The algorithm is an RNC algorithm, meaning that it is a probabilistic algorithm that runs in polylog time using a polynomial number of processors on a P-RAM. The run time of the algorithm is &Ogr;(TMM(n)log3n), and the number of processors used is PMM(n) where TMM(n) and PMM(n) are the time and number of processors needed to find a minimum weight perfect matching on an n vertex graph with maximum edge weight n.