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The Maximum Edge Weight Clique Problem: Formulations and Solution Approaches

Part of the Springer Optimization and Its Applications book series (SOIA,volume 130)

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.

Keywords

  • Maximum Edge Weight Clique (MEWC)
  • Standard Benchmark Instances
  • Broadband Network Design
  • Mathematical Optimization Formulations
  • Greedy Randomized Adaptive Search Procedure (GRASP)

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    Pullan [50] does not specify any time limit used; however for some instances, the average time reported is over 3300 s.

  2. 2.

    http://dimacs.rutgers.edu/Challenges/.

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Acknowledgments

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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Correspondence to Sergiy Butenko .

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Hosseinian, S., Fontes, D.B.M.M., Butenko, S., Nardelli, M.B., Fornari, M., Curtarolo, S. (2017). The Maximum Edge Weight Clique Problem: Formulations and Solution Approaches. In: Butenko, S., Pardalos, P., Shylo, V. (eds) Optimization Methods and Applications . Springer Optimization and Its Applications, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-68640-0_10

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