On Effectively Finding Maximal Quasi-cliques in Graphs

  • Authors:
  • Mauro Brunato;Holger H. Hoos;Roberto Battiti

  • Affiliations:
  • Dipartimento di Ingegneria e Scienza dell'Informazione, Università di Trento, Trento, Italy;Department of Computer Science, University of British Columbia, Vancouver, Canada;Dipartimento di Ingegneria e Scienza dell'Informazione, Università di Trento, Trento, Italy

  • Venue:
  • Learning and Intelligent Optimization
  • Year:
  • 2008

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Abstract

The problem of finding a maximum clique in a graph is prototypical for many clustering and similarity problems; however, in many real-world scenarios, the classical problem of finding a complete subgraph needs to be relaxed to finding an almost complete subgraph, a so-called quasi-clique . In this work, we demonstrate how two previously existing definitions of quasi-cliques can be unified and how the resulting, more general quasi-clique finding problem can be solved by extending two state-of-the-art stochastic local search algorithms for the classical maximum clique problem. Preliminary results for these algorithms applied to both, artificial and real-world problem instances demonstrate the usefulness of the new quasi-clique definition and the effectiveness of our algorithms.