Fast Parallel Algorithms for Finding Cutpoints and Bridges of Undirected Graphs

ABSTRACT In this paper we present fast parallel algorithms for finding the cutpoints and bridges of an undirected graph G = (V,E) having n vertices. We start with the notion of partitioning a graph in a set of (mutually disjoint) adjacency-level sets, and we propose a parallel algorithm which computes these sets in time O(logL) using L · H · n2 processors on a CRCW-PRAM, where L < n and H < n. Based on the properties of the adjacency-level sets, we formulate parallel algorithms which locate all cutpoints and bridges of an undirected graph in constant time O(1) by using no more than L · H · n2 processors on a CRCW-PRAM computational model.