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An efficient parallel algorithm for shortest paths in planar layered digraphs

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Abstract

Computing shortest paths in a directed graph has received considerable attention in the sequential RAM model of computation. However, developing a polylog-time parallel algorithm that is close to the sequential optimal in terms of the total work done remains an elusive goal. We present a first step in this direction by giving efficient parallel algorithms for shortest paths in planar layered digraphs.

We show that these graphs admit special kinds of separators calledone- way separators which allow the paths in the graph to cross it only once. We use these separators to give divide- and -conquer solutions to the problem of finding the shortest paths between any two vertices. We first give a simple algorithm that works in the CREW model and computes the shortest path between any two vertices in ann-node planar layered digraph in timeO(log2 n) usingn/logn processors. We then use results of Aggarwal and Park [1] and Atallah [4] to improve the time bound toO(log2 n) in the CREW model andO(logn log logn) in the CREW model. The processor bounds still remain asn/logn for the CREW model andn/log logn for the CRCW model.

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Authors and Affiliations

  1. Department of Computer Science, Brown University, 02912-1910, Providence, RI, USA

    S. Subramanian & R. Tamassia

  2. Department of Computer Science, Duke University, 27708-0129, Durham, NC, USA

    J. S. Vitter

Authors
  1. S. Subramanian
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  2. R. Tamassia
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  3. J. S. Vitter
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Additional information

Communicated by C. K. Wong.

Support for the first and third authors was provided in part by a National Science Foundation Presidential Young Investigator Award CCR-9047466 with matching funds from IBM, by NSF Research Grant CCR-9007851, by Army Research Office Grant DAAL03-91-G-0035, and by the Office of Naval Research and the Advanced Research Projects Agency under Contract N00014-91-J-4052, ARPA, Order 8225. Support for the second author was provided in part by NSF Research Grant CCR-9007851, by Army Research Office Grant DAAL03-91-G-0035, and by the Office of Naval Research and the Advanced Research Projects Agency under Contract N00014-91-J-4052 and ARPA Order 8225.

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Subramanian, S., Tamassia, R. & Vitter, J.S. An efficient parallel algorithm for shortest paths in planar layered digraphs. Algorithmica 14, 322–339 (1995). https://doi.org/10.1007/BF01294130

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  • DOI: https://doi.org/10.1007/BF01294130

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