IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v53y2012i3p649-680.html
   My bibliography  Save this article

Branch and cut algorithms for detecting critical nodes in undirected graphs

Author

Listed:
  • Marco Di Summa

    ()

  • Andrea Grosso

    ()

  • Marco Locatelli

    ()

Abstract

In this paper we deal with the critical node problem, where a given number of nodes has to be removed from an undirected graph in order to maximize the disconnections between the node pairs of the graph. We propose an integer linear programming model with a non-polynomial number of constraints but whose linear relaxation can be solved in polynomial time. We derive different valid inequalities and some theoretical results about them. We also propose an alternative model based on a quadratic reformulation of the problem. Finally, we perform many computational experiments and analyze the corresponding results. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Marco Di Summa & Andrea Grosso & Marco Locatelli, 2012. "Branch and cut algorithms for detecting critical nodes in undirected graphs," Computational Optimization and Applications, Springer, vol. 53(3), pages 649-680, December.
  • Handle: RePEc:spr:coopap:v:53:y:2012:i:3:p:649-680
    DOI: 10.1007/s10589-012-9458-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-012-9458-y
    Download Restriction: Access to full text is restricted to subscribers.

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

    Citations

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


    Cited by:

    1. Mahdavi Pajouh, Foad & Walteros, Jose L. & Boginski, Vladimir & Pasiliao, Eduardo L., 2015. "Minimum edge blocker dominating set problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 16-26.
    2. repec:eee:ejores:v:265:y:2018:i:3:p:895-908 is not listed on IDEAS
    3. repec:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-016-2110-y is not listed on IDEAS

    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:coopap:v:53:y:2012:i:3:p:649-680. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.