A random 1-011-011-01algorithm for depth first search

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 O(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. © 1988 Akadémiai Kiadó.