Elsevier

Journal of Algorithms

Volume 12, Issue 1, March 1991, Pages 110-125
Journal of Algorithms

Transitive compaction in parallel via branchings

https://doi.org/10.1016/0196-6774(91)90026-UGet rights and content

Abstract

We study the following problem: given a strongly connected digraph, find a minimal strongly connected spanning subgraph of it. Our main result is a parallel algorithm for this problem, which runs in polylog parallel time and uses O(n3) processors on a PRAM. Our algorithm is simple and the major tool it uses is computing a minimum-weight branching with zero-one weights. We also present sequential algorithms for the problem that run in time O(m + n · log n).

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    Supported in part by the International Computer Science Institute, Berkeley, California.

    1

    Current affiliation: AT & T Bell Laboratories, Murray Hill, NJ 07974.

    Also supported by NSF Grant CCR-8411954. Current affiliation: University of California at Berkeley and International Computer Science Institute, Berkeley, CA.

    2

    Current affiliation: Shell Development Company, PO Box 481, Houston, TX 77011.

    §

    Research at Princeton University partially supported by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center grant NSF-STC88-09648, and NSF Grant CCR-8920505. Current affiliation: Princeton University and NEC Research Institute, Princeton, NJ.

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