IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v337y2024i2d10.1007_s10479-024-05890-0.html
   My bibliography  Save this article

Triangle width problem: at the intersection of graph theory, scheduling, and matrix visualization

Author

Listed:
  • Khadija Hadj Salem

    (Université de Tours, LIFAT EA 6300, CNRS, ROOT ERL CNRS 7002)

  • Luc Libralesso

    (Univ. Grenoble Alpes, CNRS, Grenoble INP, G-SCOP)

  • Vincent Jost

    (Univ. Grenoble Alpes, CNRS, Grenoble INP, G-SCOP)

  • Florian Fontan

    (Univ. Grenoble Alpes, CNRS, Grenoble INP, G-SCOP)

  • Frédéric Maffray

    (Univ. Grenoble Alpes, CNRS, Grenoble INP, G-SCOP)

Abstract

This paper addresses the triangle width problem, which generalizes the classic two-machine flexible job-shop problem (FJSP) with tooling constraints. This new problem can be studied from three different angles: scheduling, matrix visualization, and vertex ordering in hypergraphs. We prove the equivalence of the different formulations of the problem and use them to establish the $$\mathcal{N}\mathcal{P}$$ N P -Hardness and polynomiality of several of its subcases. This problem allows us to find more elegant (and probably shorter) proofs for several combinatorial problems in our analysis setting. Our study provides an elegant generalization of Johnson’s argument for the two-machine flow shop. It also shows the relation between the question: “Is a matrix triangular?” and the “k-visit of a graph”.

Suggested Citation

  • Khadija Hadj Salem & Luc Libralesso & Vincent Jost & Florian Fontan & Frédéric Maffray, 2024. "Triangle width problem: at the intersection of graph theory, scheduling, and matrix visualization," Annals of Operations Research, Springer, vol. 337(2), pages 715-730, June.
    • Handle: RePEc:spr:annopr:v:337:y:2024:i:2:d:10.1007_s10479-024-05890-0
    DOI: 10.1007/s10479-024-05890-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-024-05890-0
    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/s10479-024-05890-0?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:annopr:v:337:y:2024:i:2:d:10.1007_s10479-024-05890-0. 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.