The Maximum Edge Weight Clique Problem: Formulations and Solution Approaches

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. S. Hosseinian • S. Butenko ( ) Texas A&M University, 2027 Emerging Technologies Building, Mail Stop 3131, College Station, TX 77843, USA e-mail: [email protected]; [email protected] D.B.M.M. Fontes Faculdade de Economia da Universidade do Porto, and LIAAD/INESC TEC, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal e-mail: [email protected] M.B. Nardelli Physics, Chemistry and iARTA, Initiative for Advanced Research in Technology and the Arts, University of North Texas, Denton, TX 76203, USA e-mail: [email protected] M. Fornari Department of Physics, Central Michigan University, Mount Pleasant, MI 48859, USA e-mail: [email protected] S. Curtarolo Materials Science, Electrical Engineering, Physics and Chemistry, Duke University, 144 Hudson Hall, Durham, NC 27708, USA e-mail: [email protected] © Springer International Publishing AG 2017 S. Butenko et al. (eds.), Optimization Methods and Applications, Springer Optimization and Its Applications 130, https://doi.org/10.1007/978-3-319-68640-0_10 217 218 S. Hosseinian et al.