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An Enhanced Infra-Chromatic Bound for the Maximum Clique Problem

  • Pablo San SegundoEmail author
  • Jorge Artieda
  • Rafael Leon
  • Cristobal Tapia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10122)

Abstract

There has been a rising interest in experimental exact algorithms for the maximum clique problem because the gap between the expected theoretical performance and the reported results in practice is becoming surprisingly large. One reason for this is the family of bounding functions denoted as infra-chromatic because they produce bounds which can be lower than the chromatic number of the bounded subgraph. In this paper we describe a way to enhance exact solvers with an additional infra-chromatic bounding function and report performance over a number of graphs from well known data sets. Moreover, the reported results show that the new enhanced procedure significantly outperforms state-of-the-art.

Keywords

Infra-chromatic Clique Approximate-coloring Branch-and-bound Combinatorial optimization Search 

Notes

Acknowledgments

This work is funded by the Spanish Ministry of Economy and Competitiveness (grant NAVEGASE: DPI 2014-53525-C3-1-R).

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Pablo San Segundo
    • 1
    Email author
  • Jorge Artieda
    • 1
  • Rafael Leon
    • 1
  • Cristobal Tapia
    • 1
  1. 1.Center for Automation and Robotics (CAR)Polytechnic University of Madrid (UPM)MadridSpain

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