inria-00070393, version 2
Reporting maximal cliques: new insights into an old problem
Frederic Cazals
1Chinmay Karande 1
N° RR-5615 (2006)
Résumé : Reporting maximal cliques of a graph is a fundamental problem arising many areas. Surprisingly, this problem is often tackled resorting to the old Bron-Kerbosch algorithm (1973), or its recent variant by I. Koch (2001). Both algorithms suffer from a poor output sensitivity and worst-cases. In this context, this paper makes three contributions. First, we show that a slight modification of the greedy pivoting strategy used by I. Koch allows one to get rid of worst-cases, also improving overall performances. Second, exploiting the recursive structure of non maximal cliques, we show the pivoting strategy developed by I. Koch is a particular case of a more general optimization strategy based on the concept of {\em dominated} nodes. Using different instantiations of this concept, we design four modified Bron-Kerbosch algorithms, with better output-sensitivity. Third, we discuss implementation issues and provide a detailed experimental study on random graphs. The bottom-line of this study is the investigation of the trade-off between output sensitivity and the overhead associated to the identification of dominated nodes.
- 1 : GEOMETRICA (INRIA Sophia Antipolis)
- INRIA
- Domaine : Informatique/Autre
- Mots-clés : MAXIMAL CLIQUES – SHAPE MATCHING
- Référence interne : RR-5615
- Versions disponibles : v1 (31-05-2006) v2 (30-01-2007)
- inria-00070393, version 2
- http://hal.inria.fr/inria-00070393
- oai:hal.inria.fr:inria-00070393
- Contributeur : Frederic Cazals
- Soumis le : Mardi 30 Janvier 2007, 17:28:31
- Dernière modification le : Mercredi 18 Mars 2009, 16:52:41






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