Finding strongly connected components in parallel using O(log2n) reachability queries

Authors:
Warren Schudy
Affiliations:
Brown University, Providence, RI, USA
Venue:
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Year:
2008

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Abstract

We give a randomized (Las-Vegas) parallel algorithm for computing strongly connected components of a graph with n vertices and m edges. The runtime is dominated by O(log2n) multi-source parallel reachability queries; i.e. O(log2n) calls to a subroutine that computes the union of the descendants of a given set of vertices in a given digraph. Our algorithm also topologically sorts the strongly connected components. Using Ullman and Yannakakis's [22] techniques for the reachability subroutine gives our algorithm runtime Õ(t) using mn/t2 processors for any (n2/m)1/3 ≤= t ≤= n. On sparse graphs, this improves the number of processors needed to compute strongly connected components and topological sort within time n1/3 ≤= t ≤= n from the previously best known (n/t)3 [20] to (n/t)2.