Finding Strongly Connected Components in Parallel using O(log n) Reachability Queries
نویسنده
چکیده
We give a randomized (Las-Vegas) parallel algorithm for computing strongly connected components of a graph with n vertices andm edges. The runtime is dominated byO(log n) multi-source parallel reachability queries; i.e. O(log 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 processors for any (n/m) ≤ t ≤ n. On sparse graphs, this improves the number of processors needed to compute strongly connected components and topological sort within time n ≤ t ≤ n from the previously best known (n/t) [21] to (n/t).
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