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Technical Note---On Traveling Salesman Games with Asymmetric Costs

Author

Listed:
  • Alejandro Toriello

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Nelson A. Uhan

    (Mathematics Department, United States Naval Academy, Annapolis, Maryland 21402)

Abstract

We consider cooperative traveling salesman games with nonnegative asymmetric costs satisfying the triangle inequality. We construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric traveling salesman problem, using the parsimonious property and a previously unknown connection to linear production games. We also show that our techniques extend to larger classes of network design games. We then provide a simple example showing that our cost allocation does not necessarily achieve the best possible budget balance guarantee, even among cost allocations stable for the game defined by the Held-Karp relaxation, and discuss its implications on future work on traveling salesman games.

Suggested Citation

  • Alejandro Toriello & Nelson A. Uhan, 2013. "Technical Note---On Traveling Salesman Games with Asymmetric Costs," Operations Research, INFORMS, vol. 61(6), pages 1429-1434, December.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:6:p:1429-1434
    DOI: 10.1287/opre.2013.1225
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    References listed on IDEAS

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    1. Moses Charikar & Michel X. Goemans & Howard Karloff, 2006. "On the Integrality Ratio for the Asymmetric Traveling Salesman Problem," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 245-252, May.
    2. WOLSEY, Laurence A., 1980. "Heuristic analysis, linear programming and branch and bound," LIDAM Reprints CORE 407, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Arroyo, Federico, 2024. "Cost Allocation in Vehicle Routing Problems with Time Windows," Junior Management Science (JUMS), Junior Management Science e. V., vol. 9(1), pages 1241-1268.
    3. Guajardo, Mario & Rönnqvist, Mikael & Flisberg, Patrik & Frisk, Mikael, 2018. "Collaborative transportation with overlapping coalitions," European Journal of Operational Research, Elsevier, vol. 271(1), pages 238-249.

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