Efficient Parallel and Distributed Topological Sort Algorithms

Authors:
Jun Ma;Kazuo Iwama;Tadao Takaoka;Qian-Ping Gus
Affiliations:
-;-;-;-
Venue:
PAS '97 Proceedings of the 2nd AIZU International Symposium on Parallel Algorithms / Architecture Synthesis
Year:
1997

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Abstract

Abstarct: In this paper, we give eficient parallel and distributed algomthms for the topological sort problem on acyclic graphs with n vertices. Our parallel algorithm solves the problem on a CREW PRAM in O(log2 n) time with O(M(n)/ log n) processors, where M(n) denotes the number of processors needed to multiply two n x n integer matrices over the integer ring. The best known upper bound of M(n) is O(n2.376). The parallel algorithm can also solve the problem on processor arrays with recon$gurable bus systems in O(1) time and O(n3) processors. Our distributed algorithm solves the topological sort problem of an arbitrary asynchronous network with communication complexity O(n2).