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The Maximum Edge Weight Clique Problem: Formulations and Solution Approaches

In: Optimization Methods and Applications

Author

Listed:
  • Seyedmohammadhossein Hosseinian

    (Texas A&M University)

  • Dalila B. M. M. Fontes

    (Faculdade de Economia da Universidade do Porto, and LIAAD/INESC TEC, Rua Dr. Roberto Frias)

  • Sergiy Butenko

    (Texas A&M University)

  • Marco Buongiorno Nardelli

    (University of North Texas)

  • Marco Fornari

    (Central Michigan University)

  • Stefano Curtarolo

    (Duke University)

Abstract

Given an edge-weighted graph, the maximum edge weight clique (MEWC) problem is to find a clique that maximizes the sum of edge weights within the corresponding complete subgraph. This problem generalizes the classical maximum clique problem and finds many real-world applications in molecular biology, broadband network design, pattern recognition and robotics, information retrieval, marketing, and bioinformatics among other areas. The main goal of this chapter is to provide an up-to-date review of mathematical optimization formulations and solution approaches for the MEWC problem. Information on standard benchmark instances and state-of-the-art computational results is also included.

Suggested Citation

  • Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko & Marco Buongiorno Nardelli & Marco Fornari & Stefano Curtarolo, 2017. "The Maximum Edge Weight Clique Problem: Formulations and Solution Approaches," Springer Optimization and Its Applications, in: Sergiy Butenko & Panos M. Pardalos & Volodymyr Shylo (ed.), Optimization Methods and Applications, pages 217-237, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-68640-0_10
    DOI: 10.1007/978-3-319-68640-0_10
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    Citations

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    Cited by:

    1. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2020. "A Lagrangian Bound on the Clique Number and an Exact Algorithm for the Maximum Edge Weight Clique Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 747-762, July.
    2. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2018. "A nonconvex quadratic optimization approach to the maximum edge weight clique problem," Journal of Global Optimization, Springer, vol. 72(2), pages 219-240, October.
    3. San Segundo, Pablo & Coniglio, Stefano & Furini, Fabio & Ljubić, Ivana, 2019. "A new branch-and-bound algorithm for the maximum edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 76-90.

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