IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v28y1980i4p847-858.html
   My bibliography  Save this article

Worst-Case and Probabilistic Analysis of Algorithms for a Location Problem

Author

Listed:
  • Gerard Cornuejols

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania)

  • George L. Nemhauser

    (Cornell University, Ithaca, New York)

  • Laurence A. Wolsey

    (University of Louvain, Louvain-La-Neuve, Belgium)

Abstract

We consider a location problem whose mathematical formulation is max s { z ( S ): S ⊆ N , | S | = K }, where z ( S ) = ∑ i ∈ I max j ∈ s c ij and C = ( c ij ) is any non-negative m × n matrix with row index set I and column index set N . We show that any procedure which uses matrix C only to calculate values of the function z ( S ) cannot, with a number of values polynomial in n , guarantee to find an optimal solution. However when C is the edge-vertex incidence matrix of a graph, we show that if n is suitably large and K is fixed or does not grow too rapidly with n , the K vertices of largest degree nearly always constitute an optimal solution.

Suggested Citation

  • Gerard Cornuejols & George L. Nemhauser & Laurence A. Wolsey, 1980. "Worst-Case and Probabilistic Analysis of Algorithms for a Location Problem," Operations Research, INFORMS, vol. 28(4), pages 847-858, August.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:4:p:847-858
    DOI: 10.1287/opre.28.4.847
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.28.4.847
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.28.4.847?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
    ---><---

    Citations

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


    Cited by:

    1. Refael Hassin & Eitan Zemel, 1984. "On Shortest Paths in Graphs with Random Weights," Discussion Papers 593, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Han, Qiaoming & Ye, Yinyu & Zhang, Hantao & Zhang, Jiawei, 2002. "On approximation of max-vertex-cover," European Journal of Operational Research, Elsevier, vol. 143(2), pages 342-355, December.
    3. A.A. Ageev & M.I. Sviridenko, 2004. "Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 307-328, September.
    4. Reuven Cohen & Mira Gonen, 2019. "On interval and circular-arc covering problems," Annals of Operations Research, Springer, vol. 275(2), pages 281-295, April.
    5. Reuven Cohen & Mira Gonen & Asaf Levin & Shmuel Onn, 2017. "On nonlinear multi-covering problems," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 645-659, February.

    More about this item

    Statistics

    Access and download statistics

    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:inm:oropre:v:28:y:1980:i:4:p:847-858. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.