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The x-and-y-axes travelling salesman problem

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

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712004912
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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 2 ()
    Pages: 333-345

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:333-345

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Combinatorial optimization; Polynomial-time algorithm; Computational complexity; Euclidean travelling salesman problem;

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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.
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