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A simplified algorithm for the all pairs shortest path problem with O(n 2logn) expected time

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  • Tadao Takaoka

    (University of Canterbury)

Abstract

The best known expected time for the all pairs shortest path problem on a directed graph with non-negative edge costs is O(n 2logn) by Moffat and Takaoka. Let the solution set be the set of vertices to which the given algorithm has so far established shortest paths. The Moffat-Takaoka algorithm maintains complexities before and after the critical point in balance, which is the moment when the size of the solution set is n−n/logn. In this paper, we remove the concept of critical point, whereby we make the algorithm simpler and seamless, resulting in a simpler analysis.

Suggested Citation

  • Tadao Takaoka, 2013. "A simplified algorithm for the all pairs shortest path problem with O(n 2logn) expected time," Journal of Combinatorial Optimization, Springer, vol. 25(2), pages 326-337, February.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:2:d:10.1007_s10878-012-9550-3
    DOI: 10.1007/s10878-012-9550-3
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    References listed on IDEAS

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    1. George B. Dantzig, 1960. "On the Shortest Route Through a Network," Management Science, INFORMS, vol. 6(2), pages 187-190, January.
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