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Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks

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  • Ponce, Diego
  • Puerto, Justo
  • Temprano, Francisco

Abstract

This paper deals with the k-way normalized cut problem in complex networks. It presents a methodology that uses mathematical optimization to provide mixed-integer linear programming formulations for the problem. The paper also develops a branch-and-price algorithm for the above-mentioned problem which scales better than the compact formulations. Additionally, a heuristic algorithm which is able to approximate large-scale image problems in those cases where the exact methods are not applicable is presented. Extensive computational experiments assess the usefulness of these methods to solve the k-way normalized cut problem. Finally, we have applied the minimum normalized cut objective function to the segmentation of actual images, showing the applicability of the introduced methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:316:y:2024:i:2:p:519-538
    DOI: 10.1016/j.ejor.2024.02.033
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Olivier Goldschmidt & Dorit S. Hochbaum, 1994. "A Polynomial Algorithm for the k-cut Problem for Fixed k," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 24-37, February.
    4. Baghersad, Milad & Emadikhiav, Mohsen & Huang, C. Derrick & Behara, Ravi S., 2023. "Modularity maximization to design contiguous policy zones for pandemic response," European Journal of Operational Research, Elsevier, vol. 304(1), pages 99-112.
    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. Federica Ricca & Andrea Scozzari & Bruno Simeone, 2013. "Political Districting: from classical models to recent approaches," Annals of Operations Research, Springer, vol. 204(1), pages 271-299, April.
    7. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    8. 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.
    9. Sukeda, Issey & Miyauchi, Atsushi & Takeda, Akiko, 2023. "A study on modularity density maximization: Column generation acceleration and computational complexity analysis," European Journal of Operational Research, Elsevier, vol. 309(2), pages 516-528.
    10. Samuel Deleplanque & Martine Labbé & Diego Ponce & Justo Puerto, 2020. "A Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 582-599, July.
    11. Maravalle, Maurizio & Simeone, Bruno & Naldini, Rosella, 1997. "Clustering on trees," Computational Statistics & Data Analysis, Elsevier, vol. 24(2), pages 217-234, April.
    12. Costa, Alberto, 2015. "MILP formulations for the modularity density maximization problem," European Journal of Operational Research, Elsevier, vol. 245(1), pages 14-21.
    13. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    14. Verónica Arredondo & Miguel Martínez-Panero & Teresa Peña & Federica Ricca, 2021. "Mathematical political districting taking care of minority groups," Annals of Operations Research, Springer, vol. 305(1), pages 375-402, October.
    15. G. Agarwal & D. Kempe, 2008. "Modularity-maximizing graph communities via mathematical programming," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(3), pages 409-418, December.
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