Variable neighborhood search for the maximum clique

  • Authors:

  • Pierre Hansen;Nenad Mladenović;Dragan Urošević

  • Affiliations:

  • GERAD and HEC Montréal 3000 ch. de la Côte-Sainte-Catherine, Montréal, Canada H3T 1V6;GERAD and HEC Montréal 3000 ch. de la Côte-Sainte-Catherine, Montréal, Canada H3T 1V6 and Mathematical Institute, Serbian Academy of Science, Kneza Mihajla 35, Belgrade 11000, Serbi ...;Mathematical Institute, Serbian Academy of Science, Kneza Mihajla 35, Belgrade 11000, Serbia, Montenegro, Yugoslavia

  • Venue:
  • Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
  • Year:
  • 2004

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Abstract

Maximum clique is one of the most studied NP-hard optimization problem on graphs because of its simplicity and its numerous applications. A basic variable neighborhood search heuristic for maximum clique that combines greedy with the simplicial vertex test in its descent step is proposed and tested on standard test problems from the literature. Despite its simplicity, the proposed heuristic outperforms most of the well-known approximate solution methods. Moreover, it gives solution of equal quality to those of the state-of-the-art heuristic of Battiti and Protasi in half the time.