IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v122y2003i1p163-17510.1023-a1026198523981.html
   My bibliography  Save this article

On Center Cycles in Grid Graphs

Author

Listed:
  • Les Foulds
  • Horst Hamacher
  • Anita Schöbel
  • Tadashi Yamaguchi

Abstract

Finding “good” cycles in graphs is a problem of great interest in graph theory as well as in locational analysis. We show that the center and median problems are NP-hard in general graphs. This result holds both for the variable cardinality case (i.e., all cycles of the graph are considered) and the fixed cardinality case (i.e., only cycles with a given cardinality p are feasible). Hence it is of interest to investigate special cases where the problem is solvable in polynomial time. In grid graphs, the variable cardinality case is, for instance, trivially solvable if the shape of the cycle can be chosen freely. If the shape is fixed to be a rectangle one can analyze rectangles in grid graphs with, in sequence, fixed dimension, fixed cardinality, and variable cardinality. In all cases a complete characterization of the optimal cycles and closed form expressions of the optimal objective values are given, yielding polynomial time algorithms for all cases of center rectangle problems. Finally, it is shown that center cycles can be chosen as rectangles for bounded cardinalities such that the center cycle problem in grid graphs is in these cases completely solved. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Les Foulds & Horst Hamacher & Anita Schöbel & Tadashi Yamaguchi, 2003. "On Center Cycles in Grid Graphs," Annals of Operations Research, Springer, vol. 122(1), pages 163-175, September.
    • Handle: RePEc:spr:annopr:v:122:y:2003:i:1:p:163-175:10.1023/a:1026198523981
    DOI: 10.1023/A:1026198523981
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1026198523981
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1026198523981?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:annopr:v:122:y:2003:i:1:p:163-175:10.1023/a:1026198523981. 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.