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New Polynomial Shortest Path Algorithms and Their Computational Attributes

Author

Listed:
  • Fred Glover

    (School of Business, University of Colorado, Boulder, Colorado 80303)

  • Darwin D. Klingman

    (Graduate School of Business, University of Texas, Austin, Texas 78712)

  • Nancy V. Phillips

    (Graduate School of Business, University of Texas, Austin, Texas 78712)

  • Robert F. Schneider

    (Graduate School of Business, University of Texas, Austin, Texas 78712)

Abstract

This paper presents six new variants of the polynomially bounded Partitioning Shortest Path (PSP) algorithm for finding the shortest path from one node to all other nodes in a network. Three of these variants, one for negative arc lengths, but without negative cycles, and two for nonnegative arc lengths, augment the PSP algorithm to maintain a property called sharp by Shier and Witzgall. The other three variants augment the PSP algorithm to maintain a property called near-sharp for nonnegative arc lengths. Extensive computational testing is presented on one of the sharp variants for nonnegative arc lengths and two of the near-sharp variants. The empirical results based on 4500 test problems with 90 different configurations and three different network topologies indicate that these new algorithms have excellent computational performance characteristics. Based on total solution times for the 4500 test problems, these new algorithms out-perform all other algorithms tested. In addition, one of the near-sharp algorithms strictly dominates all others on all problem topologies tested.

Suggested Citation

  • Fred Glover & Darwin D. Klingman & Nancy V. Phillips & Robert F. Schneider, 1985. "New Polynomial Shortest Path Algorithms and Their Computational Attributes," Management Science, INFORMS, vol. 31(9), pages 1106-1128, September.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:9:p:1106-1128
    DOI: 10.1287/mnsc.31.9.1106
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    Cited by:

    1. Elise D. Miller-Hooks & Hani S. Mahmassani, 2000. "Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks," Transportation Science, INFORMS, vol. 34(2), pages 198-215, May.
    2. William Costa & Britaldo Soares-Filho & Rodrigo Nobrega, 2022. "Can the Brazilian National Logistics Plan Induce Port Competitiveness by Reshaping the Port Service Areas?," Sustainability, MDPI, vol. 14(21), pages 1-18, November.
    3. Salim, V., 1997. "A comparison of shortest path algorithms in urban traffic assignment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 545-551.
    4. Hanif D. Sherali & Antoine G. Hobeika & Sasikul Kangwalklai, 2003. "Time-Dependent, Label-Constrained Shortest Path Problems with Applications," Transportation Science, INFORMS, vol. 37(3), pages 278-293, August.

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    Keywords

    shortest path algorithms;

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