IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v45y2023i3d10.1007_s10878-023-00998-8.html
   My bibliography  Save this article

A detailed introduction to a minimum-cost perfect matching algorithm based on linear programming

Author

Listed:
  • Kevin K. H. Cheung

    (Carleton University)

  • Kyel Governor

    (University of Chicago)

Abstract

Full technical details for a slightly simplified version of the minimum weight perfect matching via blossom belief propagation by Ahn, Park, Chertkov and Shin (in Advances in neural information processing systems, vol 28, Curran Associates, Inc., 2015) are provided. An example showing the necessity of a certain uniqueness assumption is given. An alternative to perturbing the edge weights to ensure the uniqueness assumption is satisfied is suggested.

Suggested Citation

  • Kevin K. H. Cheung & Kyel Governor, 2023. "A detailed introduction to a minimum-cost perfect matching algorithm based on linear programming," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-27, April.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:3:d:10.1007_s10878-023-00998-8
    DOI: 10.1007/s10878-023-00998-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-023-00998-8
    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/s10878-023-00998-8?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. William Cook & André Rohe, 1999. "Computing Minimum-Weight Perfect Matchings," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 138-148, May.
    Full references (including those not matched with items on IDEAS)

    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. D Briskorn & A Drexl, 2009. "A branch-and-price algorithm for scheduling sport leagues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 84-93, January.
    2. Alberto Caprara & Giuseppe Lancia & See-Kiong Ng, 2001. "Sorting Permutations by Reversals Through Branch-and-Price," INFORMS Journal on Computing, INFORMS, vol. 13(3), pages 224-244, August.
    3. Xu, Zhou & Rodrigues, Brian, 2017. "An extension of the Christofides heuristic for the generalized multiple depot multiple traveling salesmen problem," European Journal of Operational Research, Elsevier, vol. 257(3), pages 735-745.
    4. Vladimir Shenmaier, 2022. "Polynomial approximate discretization of geometric centers in high-dimensional Euclidean space," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 1039-1067, December.
    5. Fekete, Sandor P. & van der Veen, Jan C., 2007. "PackLib2: An integrated library of multi-dimensional packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1131-1135, December.
    6. F. Liers & G. Pardella, 2012. "Partitioning planar graphs: a fast combinatorial approach for max-cut," Computational Optimization and Applications, Springer, vol. 51(1), pages 323-344, January.
    7. Chris Walshaw, 2002. "A Multilevel Approach to the Travelling Salesman Problem," Operations Research, INFORMS, vol. 50(5), pages 862-877, October.

    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:jcomop:v:45:y:2023:i:3:d:10.1007_s10878-023-00998-8. 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.