IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v312y2024i1p117-124.html
   My bibliography  Save this article

A branch-and-cut algorithm for the connected max-k-cut problem

Author

Listed:
  • Healy, Patrick
  • Jozefowiez, Nicolas
  • Laroche, Pierre
  • Marchetti, Franc
  • Martin, Sébastien
  • Róka, Zsuzsanna

Abstract

The Connected Max-k-Cut Problem is an extension of the well-known Max-Cut Problem. The objective is to partition a graph into k connected subgraphs by maximizing the cost of inter-partition edges. We propose a new integer linear program for the problem and a branch-and-cut algorithm. We also explore graph isomorphism to structure the instances and facilitate their resolution. We conduct extensive computational experiments on both randomly generated instances and instances from the literature where we compare the quality of our method against existing algorithms. The experimental results show that, if k>2, our approach strictly outperforms those from the literature.

Suggested Citation

  • Healy, Patrick & Jozefowiez, Nicolas & Laroche, Pierre & Marchetti, Franc & Martin, Sébastien & Róka, Zsuzsanna, 2024. "A branch-and-cut algorithm for the connected max-k-cut problem," European Journal of Operational Research, Elsevier, vol. 312(1), pages 117-124.
    • Handle: RePEc:eee:ejores:v:312:y:2024:i:1:p:117-124
    DOI: 10.1016/j.ejor.2023.06.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722172300468X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.06.015?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. Benati, Stefano & Puerto, Justo & Rodríguez-Chía, Antonio M., 2017. "Clustering data that are graph connected," European Journal of Operational Research, Elsevier, vol. 261(1), pages 43-53.
    2. Benati, Stefano & Ponce, Diego & Puerto, Justo & Rodríguez-Chía, Antonio M., 2022. "A branch-and-price procedure for clustering data that are graph connected," European Journal of Operational Research, Elsevier, vol. 297(3), pages 817-830.
    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. Ponce, Diego & Puerto, Justo & Temprano, Francisco, 2024. "Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks," European Journal of Operational Research, Elsevier, vol. 316(2), pages 519-538.
    2. Calvino, José J. & López-Haro, Miguel & Muñoz-Ocaña, Juan M. & Puerto, Justo & Rodríguez-Chía, Antonio M., 2022. "Segmentation of scanning-transmission electron microscopy images using the ordered median problem," European Journal of Operational Research, Elsevier, vol. 302(2), pages 671-687.
    3. Vangerven, Bart & Briskorn, Dirk & Goossens, Dries R. & Spieksma, Frits C.R., 2022. "Parliament seating assignment problems," European Journal of Operational Research, Elsevier, vol. 296(3), pages 914-926.
    4. Blanco, Víctor & Gázquez, Ricardo & Ponce, Diego & Puerto, Justo, 2023. "A branch-and-price approach for the continuous multifacility monotone ordered median problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 105-126.
    5. Benati, Stefano & Ponce, Diego & Puerto, Justo & Rodríguez-Chía, Antonio M., 2022. "A branch-and-price procedure for clustering data that are graph connected," European Journal of Operational Research, Elsevier, vol. 297(3), pages 817-830.
    6. Alessandro Avellone & Stefano Benati & Rosanna Grassi & Giorgio Rizzini, 2022. "On Finding the Community with Maximum Persistence Probability," Papers 2206.10330, arXiv.org.
    7. Rota Bulò, Samuel & Pelillo, Marcello, 2017. "Dominant-set clustering: A review," European Journal of Operational Research, Elsevier, vol. 262(1), pages 1-13.
    8. Benati, Stefano & Puerto, Justo & Rodríguez-Chía, Antonio M. & Temprano, Francisco, 2022. "A mathematical programming approach to overlapping community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    9. Victor Blanco & Alberto Japón & Justo Puerto, 2022. "Robust optimal classification trees under noisy labels," 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(1), pages 155-179, March.
    10. Arcagni, Alberto & Grassi, Rosanna & Stefani, Silvana & Torriero, Anna, 2017. "Higher order assortativity in complex networks," European Journal of Operational Research, Elsevier, vol. 262(2), pages 708-719.
    11. Albareda-Sambola, Maria & Marín, Alfredo & Rodríguez-Chía, Antonio M., 2019. "Reformulated acyclic partitioning for rail-rail containers transshipment," European Journal of Operational Research, Elsevier, vol. 277(1), pages 153-165.
    12. Zhu, Shan & Hu, Xiangpei & Huang, Kai & Yuan, Yufei, 2021. "Optimization of product category allocation in multiple warehouses to minimize splitting of online supermarket customer orders," European Journal of Operational Research, Elsevier, vol. 290(2), pages 556-571.
    13. Luisa I. Martínez-Merino & Diego Ponce & Justo Puerto, 2023. "Constraint relaxation for the discrete ordered median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 538-561, 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:eee:ejores:v:312:y:2024:i:1:p:117-124. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.