IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v32y2020i2p279-288.html
   My bibliography  Save this article

Solving the Nearly Symmetric All-Pairs Shortest-Path Problem

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2018.0873
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2018.0873?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, April.
    2. Gutierrez, Genaro J. & Kouvelis, Panagiotis & Kurawarwala, Abbas A., 1996. "A robustness approach to uncapacitated network design problems," European Journal of Operational Research, Elsevier, vol. 94(2), pages 362-376, October.
    3. Meyr, H., 2000. "Simultaneous lotsizing and scheduling by combining local search with dual reoptimization," European Journal of Operational Research, Elsevier, vol. 120(2), pages 311-326, January.
    4. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    5. Mijangos, E., 2005. "An efficient method for nonlinearly constrained networks," European Journal of Operational Research, Elsevier, vol. 161(3), pages 618-635, March.
    6. Balaji Gopalakrishnan & Seunghyun Kong & Earl Barnes & Ellis Johnson & Joel Sokol, 2011. "A least-squares minimum-cost network flow algorithm," Annals of Operations Research, Springer, vol. 186(1), pages 119-140, June.
    7. Festa, P. & Guerriero, F. & Laganà, D. & Musmanno, R., 2013. "Solving the shortest path tour problem," European Journal of Operational Research, Elsevier, vol. 230(3), pages 464-474.
    8. Yves Pochet & Mathieu Van Vyve, 2004. "A General Heuristic for Production Planning Problems," INFORMS Journal on Computing, INFORMS, vol. 16(3), pages 316-327, August.
    9. R. Fourer & H. Gassmann & J. Ma & R. Martin, 2009. "An XML-based schema for stochastic programs," Annals of Operations Research, Springer, vol. 166(1), pages 313-337, February.
    10. Maya Duque, Pablo A. & Coene, Sofie & Goos, Peter & Sörensen, Kenneth & Spieksma, Frits, 2013. "The accessibility arc upgrading problem," European Journal of Operational Research, Elsevier, vol. 224(3), pages 458-465.
    11. ÇalIskan, Cenk, 2011. "A specialized network simplex algorithm for the constrained maximum flow problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 137-147, April.
    12. Mongeau, Marcel & Sartenaer, Annick, 1995. "Automatic decrease of the penalty parameter in exact penalty function methods," European Journal of Operational Research, Elsevier, vol. 83(3), pages 686-699, June.
    13. Mesquita-Cunha, Mariana & Figueira, José Rui & Barbosa-Póvoa, Ana Paula, 2023. "New ϵ−constraint methods for multi-objective integer linear programming: A Pareto front representation approach," European Journal of Operational Research, Elsevier, vol. 306(1), pages 286-307.
    14. Granat, Janusz & Guerriero, Francesca, 2003. "The interactive analysis of the multicriteria shortest path problem by the reference point method," European Journal of Operational Research, Elsevier, vol. 151(1), pages 103-118, November.
    15. Moreno, Alfredo & Munari, Pedro & Alem, Douglas, 2019. "A branch-and-Benders-cut algorithm for the Crew Scheduling and Routing Problem in road restoration," European Journal of Operational Research, Elsevier, vol. 275(1), pages 16-34.
    16. Larsson, Torbjörn & Marklund, Johan & Olsson, Caroline & Patriksson, Michael, 2008. "Convergent Lagrangian heuristics for nonlinear minimum cost network flows," European Journal of Operational Research, Elsevier, vol. 189(2), pages 324-346, September.
    17. P. Beraldi & F. Guerriero & R. Musmanno, 1997. "Efficient Parallel Algorithms for the Minimum Cost Flow Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 501-530, December.
    18. Dayal Madhukar & Verma, Sanjay, 2015. "Multi-processor Exact Procedures for Regular Measures of the Multi-mode RCPSP," IIMA Working Papers WP2015-03-25, Indian Institute of Management Ahmedabad, Research and Publication Department.
    19. Ahuja, Ravindra K., 1956- & Orlin, James B., 1953-, 1992. "Use of representative operation counts in computational testings of algorithms," Working papers 3459-92., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    20. David R. Morrison & Jason J. Sauppe & Sheldon H. Jacobson, 2013. "A Network Simplex Algorithm for the Equal Flow Problem on a Generalized Network," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 2-12, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orijoc:v:32:y:2020:i:2:p:279-288. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.