IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v90y2025i2d10.1007_s10589-024-00637-w.html
   My bibliography  Save this article

A branch-and-price algorithm for the hyper-rectangular clustering problem with axis-parallel clusters and outliers

Author

Listed:
  • Diego Delle Donne

    (ESSEC Business School)

  • Javier Marenco

    (Universidad Torcuato Di Tella)

Abstract

We address the problem of clustering a set of points in $$\mathbb {R}^d$$ R d with axis-parallel clusters, while allowing to discard a pre-specified number of points, thus declared to be outliers. We present an integer programming formulation for this problem which employs exponentially-many variables and we develop an exact algorithm to solve it, based on branch-and-price techniques. We solve the linear relaxation of the proposed model by applying column generation and we propose two different integer programming formulations to tackle the associated pricing subproblem. For the branch-and-price algorithm, we propose a branching rule specifically tailored for the problem. Finally, we provide computational experiments showing that the proposed approach is effective in practice.

Suggested Citation

  • Diego Delle Donne & Javier Marenco, 2025. "A branch-and-price algorithm for the hyper-rectangular clustering problem with axis-parallel clusters and outliers," Computational Optimization and Applications, Springer, vol. 90(2), pages 583-605, March.
    • Handle: RePEc:spr:coopap:v:90:y:2025:i:2:d:10.1007_s10589-024-00637-w
    DOI: 10.1007/s10589-024-00637-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-024-00637-w
    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/s10589-024-00637-w?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:coopap:v:90:y:2025:i:2:d:10.1007_s10589-024-00637-w. 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.