Speeding up branch and bound algorithms for solving the maximum clique problem

  • Authors:

  • Evgeny Maslov;Mikhail Batsyn;Panos M. Pardalos

  • Affiliations:

  • Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics, Niznhy Novgorod, Russia;Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics, Niznhy Novgorod, Russia;Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics, Niznhy Novgorod, Russia and Center of Applied Optimization, University of ...

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2014

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Abstract

In this paper we consider two branch and bound algorithms for the maximum clique problem which demonstrate the best performance on DIMACS instances among the existing methods. These algorithms are MCS algorithm by Tomita et al. (2010) and MAXSAT algorithm by Li and Quan (2010a, b). We suggest a general approach which allows us to speed up considerably these branch and bound algorithms on hard instances. The idea is to apply a powerful heuristic for obtaining an initial solution of high quality. This solution is then used to prune branches in the main branch and bound algorithm. For this purpose we apply ILS heuristic by Andrade et al. (J Heuristics 18(4):525---547, 2012). The best results are obtained for p_hat1000-3 instance and gen instances with up to 11,000 times speedup.