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Solving the Nearly Symmetric All-Pairs Shortest-Path Problem

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  • Gerald G. Brown

    (Naval Postgraduate School, Monterey, California 93943)

  • W. Matthew Carlyle

    (Naval Postgraduate School, Monterey, California 93943)

Abstract

We introduce a simple modification to the repeated shortest-path algorithm for the all-pairs shortest-path problem that adds a cumulative distance label update at each iteration based on the shortest-path tree from the prior iteration. We have implemented and tested our update using several shortest-path algorithms on a range of test networks of varying size, degree, and “skewness” (i.e., asymmetry) of costs on antisymmetric arcs, and we find that it provides a significant speedup to any such algorithm, except for cases either in which the underlying graph is extremely sparsely connected (or even disconnected) or when the arc costs are highly nonsymmetric. An added charm is that our best-modified method preserves the polynomial worst case runtime of its label-correcting antecedent. As with other repeated shortest-path algorithms, it is significantly faster than the Floyd–Warshall algorithm on sparsely connected networks and even some fairly densely connected networks.

Suggested Citation

  • Gerald G. Brown & W. Matthew Carlyle, 2020. "Solving the Nearly Symmetric All-Pairs Shortest-Path Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 279-288, April.
  • Handle: RePEc:inm:orijoc:v:32:y:2020:i:2:p:279-288
    DOI: 10.1287/ijoc.2018.0873
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    References listed on IDEAS

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    1. F. Glover & D. Klingman & N. Phillips, 1985. "A New Polynomially Bounded Shortest Path Algorithm," Operations Research, INFORMS, vol. 33(1), pages 65-73, February.
    2. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    3. Gordon H. Bradley & Gerald G. Brown & Glenn W. Graves, 1977. "Exceptional Paper--Design and Implementation of Large Scale Primal Transshipment Algorithms," Management Science, INFORMS, vol. 24(1), pages 1-34, September.
    4. Alan Washburn & Gerald G. Brown, 2016. "An exact method for finding shortest routes on a sphere, avoiding obstacles," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(5), pages 374-385, August.
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    Cited by:

    1. Zhang, Dongqing & Wallace, Stein W. & Guo, Zhaoxia & Dong, Yucheng & Kaut, Michal, 2021. "On scenario construction for stochastic shortest path problems in real road networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).

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