Work-efficient BSR-based parallel algorithms for some fundamental problems in graph theory

Abstract

This paper presents BSR-parallel algorithms for some problems in fundamental graph theory : transitive closure, connected components, spanning tree, bridges and articulation points of a graph and bipartite graph recognition. There already exist constant time algorithms to solve these problems on a mesh with reconfigurable bus system using O(N 4) processors. Here we show that these problems can be solved in constant time using only O(N 2) processors on the BSR model (N is the number of vertices of the graph G). Therefore, our algorithms are more work-efficient. These new results suggest that many other problems in graph theory can be solved in constant time using the BSR model.