Efficient parallel and distributed topological sort algorithms

In this paper, we give efficient parallel and distributed algorithms 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×n integer matrices over the integer ring. The best known upper bound of M(n) is O(n^2.376). The parallel algorithm can also solve the problem on processor arrays with reconfigurable 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)