IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v26y2023i6d10.1007_s10951-021-00680-z.html
   My bibliography  Save this article

Scheduling on a graph with release times

Author

Listed:
  • Wei Yu

    (East China University of Science and Technology)

  • Mordecai Golin

    (Hong Kong University of Science and Technology)

  • Guochuan Zhang

    (Zhejiang University)

Abstract

We study a generalization of the well-known traveling salesman problem in a metric space, in which each city is associated with a release time. The salesman has to visit each city at or after its release time. There exists a naive 5/2-approximation algorithm where the salesman simply starts to route the network after all cities are released. Interestingly, this bound has never been improved for more than two decades. In this paper, we revisit the problem and achieve the following results. First, we devise an approximation algorithm with performance ratio less than 5/2 when the number of distinct release times is fixed. Then, we analyze a natural class of algorithms and show that no performance ratio better than 5/2 is possible unless the Metric TSP can be approximated with a ratio strictly less than 3/2, which is a well-known longstanding open question. Finally, we consider a special case where the graph has a heavy edge and present an approximation algorithm with performance ratio less than 5/2.

Suggested Citation

  • Wei Yu & Mordecai Golin & Guochuan Zhang, 2023. "Scheduling on a graph with release times," Journal of Scheduling, Springer, vol. 26(6), pages 571-580, December.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:6:d:10.1007_s10951-021-00680-z
    DOI: 10.1007/s10951-021-00680-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-021-00680-z
    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/s10951-021-00680-z?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.

    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:jsched:v:26:y:2023:i:6:d:10.1007_s10951-021-00680-z. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.