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Improved integrality gap upper bounds for traveling salesperson problems with distances one and two

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  • Mnich, Matthias
  • Mömke, Tobias

Abstract

We prove new integrality gap upper bounds for the traveling salesperson problem with distances one and two ((1,2)-TSP). We obtain these bounds by investigating the structure of the support graph of optimal solutions to the subtour elimination linear programming relaxation, with one additional cutting plane inequality.

Suggested Citation

  • Mnich, Matthias & Mömke, Tobias, 2018. "Improved integrality gap upper bounds for traveling salesperson problems with distances one and two," European Journal of Operational Research, Elsevier, vol. 266(2), pages 436-457.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:436-457
    DOI: 10.1016/j.ejor.2017.09.036
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    References listed on IDEAS

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    1. Christos H. Papadimitriou & Mihalis Yannakakis, 1993. "The Traveling Salesman Problem with Distances One and Two," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 1-11, February.
    2. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    3. M. L. Balinski, 1965. "Integer Programming: Methods, Uses, Computations," Management Science, INFORMS, vol. 12(3), pages 253-313, November.
    4. Frans Schalekamp & David P. Williamson & Anke van Zuylen, 2014. "2-Matchings, the Traveling Salesman Problem, and the Subtour LP: A Proof of the Boyd-Carr Conjecture," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 403-417, May.
    5. 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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