The Maximum Edge Weight Clique Problem: Formulations and Solution Approaches

  • Seyedmohammadhossein Hosseinian
  • Dalila B. M. M. Fontes
  • Sergiy Butenko
  • Marco Buongiorno Nardelli
  • Marco Fornari
  • Stefano Curtarolo
Part of the Springer Optimization and Its Applications book series (SOIA, volume 130)


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.



This work was carried out, while the second author was a visiting scholar at Texas A&M University, College Station, TX, USA, and is partially supported by scholarship SFRH/BSAB/113662/2015. Partial support by DOD-ONR (N00014-13-1-0635) NSF (CMMI-1538493) grants is also gratefully acknowledged.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Seyedmohammadhossein Hosseinian
    • 1
  • Dalila B. M. M. Fontes
    • 2
  • Sergiy Butenko
    • 1
  • Marco Buongiorno Nardelli
    • 3
  • Marco Fornari
    • 4
  • Stefano Curtarolo
    • 5
  1. 1.Texas A&M UniversityCollege StationUSA
  2. 2.Faculdade de Economia da Universidade do Porto, and LIAAD/INESC TEC, Rua Dr. Roberto FriasPortoPortugal
  3. 3.Physics, Chemistry and iARTA, Initiative for Advanced Research in Technology and the ArtsUniversity of North TexasDentonUSA
  4. 4.Department of PhysicsCentral Michigan UniversityMount PleasantUSA
  5. 5.Materials Science, Electrical Engineering, Physics and ChemistryDuke UniversityDurhamUSA

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