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Simple paths with exact and forbidden lengths

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  • Alexandre Dolgui
  • Mikhail Y. Kovalyov
  • Alain Quilliot

Abstract

We study new decision and optimization problems of finding a simple path between two given vertices in an arc weighted directed multigraph such that the path length is equal to a given number or it does not fall into the given forbidden intervals (gaps). A fairly complete computational complexity classification is provided and exact and approximation algorithms are suggested.

Suggested Citation

  • Alexandre Dolgui & Mikhail Y. Kovalyov & Alain Quilliot, 2018. "Simple paths with exact and forbidden lengths," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 78-85, February.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:1:p:78-85
    DOI: 10.1002/nav.21783
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    References listed on IDEAS

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    1. Peter Brucker & Mikhail Kovalyov & Yakov Shafransky & Frank Werner, 1998. "Batch scheduling with deadlines on parallel machines," Annals of Operations Research, Springer, vol. 83(0), pages 23-40, October.
    2. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms," Transportation Science, INFORMS, vol. 39(1), pages 104-118, February.
    3. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    4. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part II: Metaheuristics," Transportation Science, INFORMS, vol. 39(1), pages 119-139, February.
    5. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
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    Cited by:

    1. Soriano, Adria & Vidal, Thibaut & Gansterer, Margaretha & Doerner, Karl, 2020. "The vehicle routing problem with arrival time diversification on a multigraph," European Journal of Operational Research, Elsevier, vol. 286(2), pages 564-575.

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