Towards overcoming the transitive-closure bottleneck: Efficient parallel algorithms for planar digraphs

Ming-Yang Kao, Philip N. Klein
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
Currently, there is a significant gap between the best sequential and parallel complexities of many fundamental problems related to digraph reachability. This complexity bottleneck essentially reflects a seemingly unavoidable reliance on transitive closure techniques in parallel algorithms for digraph reachability. To pinpoint the nature of the bottleneck, we de* velop a collection of polylog-time reductions among reachability problems. These reductions use only linear processors and work for
more &raquo; ... neral graphs. Furthermore, for planar digraphs, we give polylog-time algorithms for the following problems: (1) directed ear decomposition, (2) topological ordering, (3) digraph reachability, (4) descendent counting, and (5) depth-first search. These algorithms use only linear processors and therefore reduce the complexity to within a polylog factor of optimal.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0022-0000(93)90042-u">doi:10.1016/0022-0000(93)90042-u</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4jb5tnrxobdldlrbnzbzqa2wfy">fatcat:4jb5tnrxobdldlrbnzbzqa2wfy</a> </span>
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