IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v223y2012i2p333-345.html
   My bibliography  Save this article

The x-and-y-axes travelling salesman problem

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712004912
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.06.036?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Özgür Özpeynirci & Murat Köksalan, 2010. "Pyramidal tours and multiple objectives," Journal of Global Optimization, Springer, vol. 48(4), pages 569-582, December.
    2. Vahid Riahi & Morteza Kazemi, 2018. "A new hybrid ant colony algorithm for scheduling of no-wait flowshop," Operational Research, Springer, vol. 18(1), pages 55-74, April.
    3. Lin, Shih-Wei & Ying, Kuo-Ching, 2016. "Optimization of makespan for no-wait flowshop scheduling problems using efficient matheuristics," Omega, Elsevier, vol. 64(C), pages 115-125.
    4. Smutnicki, Czeslaw & Pempera, Jaroslaw & Bocewicz, Grzegorz & Banaszak, Zbigniew, 2022. "Cyclic flow-shop scheduling with no-wait constraints and missing operations," European Journal of Operational Research, Elsevier, vol. 302(1), pages 39-49.
    5. Delorme, Xavier & Dolgui, Alexandre & Kovalev, Sergey & Kovalyov, Mikhail Y., 2019. "Minimizing the number of workers in a paced mixed-model assembly line," European Journal of Operational Research, Elsevier, vol. 272(1), pages 188-194.
    6. Kravchenko, Svetlana A., 1998. "A polynomial algorithm for a two-machine no-wait job-shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 106(1), pages 101-107, April.
    7. Lieshout, P.M.D. & Volgenant, A., 2007. "A branch-and-bound algorithm for the singly constrained assignment problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 151-164, January.
    8. Kalczynski, Pawel J. & Kamburowski, Jerzy, 2009. "An empirical analysis of the optimality rate of flow shop heuristics," European Journal of Operational Research, Elsevier, vol. 198(1), pages 93-101, October.
    9. A.J. Scott, 1969. "Combinatorial Programming and the Planning of Urban and Regional Systems," Environment and Planning A, , vol. 1(2), pages 125-142, December.
    10. He, Xuan & Pan, Quan-Ke & Gao, Liang & Neufeld, Janis S., 2023. "An asymmetric traveling salesman problem based matheuristic algorithm for flowshop group scheduling problem," European Journal of Operational Research, Elsevier, vol. 310(2), pages 597-610.
    11. Hughes, Michael S. & Lunday, Brian J. & Weir, Jeffrey D. & Hopkinson, Kenneth M., 2021. "The multiple shortest path problem with path deconfliction," European Journal of Operational Research, Elsevier, vol. 292(3), pages 818-829.
    12. Pranzo, Marco, 2004. "Batch scheduling in a two-machine flow shop with limited buffer and sequence independent setup times and removal times," European Journal of Operational Research, Elsevier, vol. 153(3), pages 581-592, March.
    13. 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.
    14. Chauhan, Satyaveer S. & Gordon, Valery & Proth, Jean-Marie, 2007. "Scheduling in supply chain environment," European Journal of Operational Research, Elsevier, vol. 183(3), pages 961-970, December.
    15. Carlier, Jacques & Haouari, Mohamed & Kharbeche, Mohamed & Moukrim, Aziz, 2010. "An optimization-based heuristic for the robotic cell problem," European Journal of Operational Research, Elsevier, vol. 202(3), pages 636-645, May.
    16. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    17. Konrad Stephan & Nils Boysen, 2017. "Crane scheduling in railway yards: an analysis of computational complexity," Journal of Scheduling, Springer, vol. 20(5), pages 507-526, October.
    18. C. A. Glass & J. N. D. Gupta & C. N. Potts, 1999. "Two-Machine No-Wait Flow Shop Scheduling with Missing Operations," Mathematics of Operations Research, INFORMS, vol. 24(4), pages 911-924, November.
    19. Waldherr, Stefan & Knust, Sigrid, 2015. "Complexity results for flow shop problems with synchronous movement," European Journal of Operational Research, Elsevier, vol. 242(1), pages 34-44.
    20. Yenisey, Mehmet Mutlu & Yagmahan, Betul, 2014. "Multi-objective permutation flow shop scheduling problem: Literature review, classification and current trends," Omega, Elsevier, vol. 45(C), pages 119-135.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:333-345. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.