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.
Holger Hoos acknowledges support provided by the Natural Sciences and Engineering Research Council of Canada (nSERC) under Discovery Grant 238788-05; Mauro Brunato and Roberto Battiti acknowledge support by the project CASCADAS (IST-027807) funded by the FET Program of the European Commission.
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© 2008 Springer-Verlag Berlin Heidelberg
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Brunato, M., Hoos, H.H., Battiti, R. (2008). On Effectively Finding Maximal Quasi-cliques in Graphs. In: Maniezzo, V., Battiti, R., Watson, JP. (eds) Learning and Intelligent Optimization. LION 2007. Lecture Notes in Computer Science, vol 5313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92695-5_4
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DOI: https://doi.org/10.1007/978-3-540-92695-5_4
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