@MISC{Schudy_nonnumericalalgorithms, author = {Warren Schudy}, title = {Nonnumerical Algorithms and Problems—Computations}, year = {} }

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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(log 2 n) multi-source parallel reachability queries; i.e. O(log 2 n) 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 [23] techniques for the reachability subroutine gives our algorithm runtime Õ(t) using mn/t 2 processors for any (n 2 /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 n 1/3 ≤ t ≤ n from the previously best known (n/t) 3 [21] to (n/t) 2.