Parallel transitive closure algorithm

Abstract

Using the BSP/CGM model, with p processors, where p n, we present a parallel algorithm to compute the transitive closure of a digraph D with n vertices and m edges. Our algorithm uses log p + 1 communication rounds if the input is an acyclic directed graph labeled using a linear extension. For general digraphs, the algorithm requires p communication rounds in the worst case. In both cases, O(M/ p) local computation is performed per round, where M is the amount of computation needed to compute a sequential transitive closure of a digraph. The presented algorithm can be implemented using any sequential algorithm that computes the transitive closure of a digraph D.