IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v69y2018i1d10.1007_s10589-017-9945-2.html
   My bibliography  Save this article

A multilevel bilinear programming algorithm for the vertex separator problem

Author

Listed:
  • William W. Hager

    (University of Florida)

  • James T. Hungerford

    (RaceTrac Store Support Center)

  • Ilya Safro

    (Clemson University)

Abstract

The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. The Vertex Separator Problem was formulated in the paper 10.1016/j.ejor.2014.05.042 as a continuous (non-concave/non-convex) bilinear quadratic program. In this paper, we develop a more general continuous bilinear program which incorporates vertex weights, and which applies to the coarse graphs that are generated in a multilevel compression of the original Vertex Separator Problem. We develop a method for improving upon a given vertex separator by applying a Mountain Climbing Algorithm to the bilinear program using an incidence vector for the separator as a starting guess. Sufficient conditions are developed under which the algorithm can improve upon the starting guess after at most two iterations. The refinement algorithm is augmented with a perturbation technique to enable escapes from local optima and is embedded in a multilevel framework for solving large scale instances of the problem. The multilevel algorithm is shown through computational experiments to perform particularly well on communication and collaboration networks.

Suggested Citation

  • William W. Hager & James T. Hungerford & Ilya Safro, 2018. "A multilevel bilinear programming algorithm for the vertex separator problem," Computational Optimization and Applications, Springer, vol. 69(1), pages 189-223, January.
    • Handle: RePEc:spr:coopap:v:69:y:2018:i:1:d:10.1007_s10589-017-9945-2
    DOI: 10.1007/s10589-017-9945-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-017-9945-2
    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/s10589-017-9945-2?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. Hager, William W. & Hungerford, James T., 2015. "Continuous quadratic programming formulations of optimization problems on graphs," European Journal of Operational Research, Elsevier, vol. 240(2), pages 328-337.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Norberto Castillo-García & Paula Hernández Hernández, 2019. "Two new integer linear programming formulations for the vertex bisection problem," Computational Optimization and Applications, Springer, vol. 74(3), pages 895-918, December.
    2. Xinxin Li & Ting Kei Pong & Hao Sun & Henry Wolkowicz, 2021. "A strictly contractive Peaceman-Rachford splitting method for the doubly nonnegative relaxation of the minimum cut problem," Computational Optimization and Applications, Springer, vol. 78(3), pages 853-891, April.

    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. Benlic, Una & Epitropakis, Michael G. & Burke, Edmund K., 2017. "A hybrid breakout local search and reinforcement learning approach to the vertex separator problem," European Journal of Operational Research, Elsevier, vol. 261(3), pages 803-818.

    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:69:y:2018:i:1:d:10.1007_s10589-017-9945-2. 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.