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The x-and-y-axes travelling salesman problem

Author

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  • Çela, Eranda
  • Deineko, Vladimir
  • Woeginger, Gerhard J.

Abstract

The x-and-y-axes travelling salesman problem forms a special case of the Euclidean TSP, where all cities are situated on the x-axis and on the y-axis of an orthogonal coordinate system of the Euclidean plane. By carefully analyzing the underlying combinatorial and geometric structures, we show that this problem can be solved in polynomial time. The running time of the resulting algorithm is quadratic in the number of cities.

Suggested Citation

  • Çela, Eranda & Deineko, Vladimir & Woeginger, Gerhard J., 2012. "The x-and-y-axes travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 333-345.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:333-345
    DOI: 10.1016/j.ejor.2012.06.036
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    References listed on IDEAS

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    1. van Dal, Rene & van der Veen, Jack A. A. & Sierksma, Gerard, 1993. "Small and large TSP: Two polynomially solvable cases of the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 69(1), pages 107-120, August.
    2. van der Veen, Jack A. A. & Sierksma, Gerard & van Dal, Rene, 1991. "Pyramidal tours and the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 52(1), pages 90-102, May.
    3. Özpeynirci, Özgür & Köksalan, Murat, 2009. "Multiobjective traveling salesperson problem on Halin graphs," European Journal of Operational Research, Elsevier, vol. 196(1), pages 155-161, July.
    4. Bagchi, Tapan P. & Gupta, Jatinder N.D. & Sriskandarajah, Chelliah, 2006. "A review of TSP based approaches for flowshop scheduling," European Journal of Operational Research, Elsevier, vol. 169(3), pages 816-854, March.
    5. Oda, Yoshiaki, 2002. "An asymmetric analog of van der Veen conditions and the traveling salesman problem (II)," European Journal of Operational Research, Elsevier, vol. 138(1), pages 43-62, April.
    6. P. C. Gilmore & R. E. Gomory, 1964. "Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem," Operations Research, INFORMS, vol. 12(5), pages 655-679, October.
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    Cited by:

    1. Wang, Zutong & Guo, Jiansheng & Zheng, Mingfa & Wang, Ying, 2015. "Uncertain multiobjective traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 241(2), pages 478-489.

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