An improved parallel algorithm that computes the BFS numbering of a directed graph

Abstract

This paper presents a parallel algorithm that computes the breadth-first search (BFS) numbering of a directed graph in O(log 2 n) time using M(n) processors on the exclusive-read exclusive-write (EREW) parallel random access machine (PRAM) model, where M(n) denotes the number of processors needed to multiply two n x n integer matrices over the ring ( Z , +, x) in O(log n) time. The best known bound for M(n) is O( n 2.376) (Coppersmith and Winograd, 1987). The algorithm presented in their paper uses fewer processors than the classical algorithm for BFS that employs matrix powering over the semiring (dioid) ( N , min, +), using O(log n) time and O( n 3) processors on the concurrent-read concurrent-write (CRCW) model, or using O(log 2 n) time and n 3 ⧸log n processors on the EREW model.