IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v181y2019i2d10.1007_s10957-018-01465-9.html
   My bibliography  Save this article

Sufficient and Necessary Conditions for an Edge in the Optimal Hamiltonian Cycle Based on Frequency Quadrilaterals

Author

Listed:
  • Yong Wang

    (North China Electric Power University)

Abstract

The symmetric traveling salesman problem is studied according to frequency graphs computed with frequency quadrilaterals. Here, we provide the sufficient and necessary conditions for an optimal Hamiltonian cycle edge based on frequency quadrilaterals. If the probability that an edge has frequency 5 in a frequency quadrilateral is 1, it belongs to the optimal Hamiltonian cycle. For an optimal Hamiltonian cycle edge, the probability that it has frequency 5 in a frequency quadrilateral tends to 1 as the scale of traveling salesman problem is sufficiently large.

Suggested Citation

  • Yong Wang, 2019. "Sufficient and Necessary Conditions for an Edge in the Optimal Hamiltonian Cycle Based on Frequency Quadrilaterals," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 671-683, May.
  • Handle: RePEc:spr:joptap:v:181:y:2019:i:2:d:10.1007_s10957-018-01465-9
    DOI: 10.1007/s10957-018-01465-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-01465-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-018-01465-9?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. Xu, Zhou & Rodrigues, Brian, 2017. "An extension of the Christofides heuristic for the generalized multiple depot multiple traveling salesmen problem," European Journal of Operational Research, Elsevier, vol. 257(3), pages 735-745.
    Full references (including those not matched with items on IDEAS)

    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. Bérczi, Kristóf & Mnich, Matthias & Vincze, Roland, 2023. "Approximations for many-visits multiple traveling salesman problems," Omega, Elsevier, vol. 116(C).
    2. Xiaofan Lai & Liang Xu & Zhou Xu & Yang Du, 2023. "An Approximation Algorithm for k -Depot Split Delivery Vehicle Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1179-1194, September.
    3. Henan Liu & Huili Zhang & Yi Xu, 2021. "The m-Steiner Traveling Salesman Problem with online edge blockages," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 844-860, May.

    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:spr:joptap:v:181:y:2019:i:2:d:10.1007_s10957-018-01465-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.