Column generation algorithms for exact modularity maximization in networks

Finding modules, or clusters, in networks currently attracts much attention in several domains. The most studied criterion for doing so, due to Newman and Girvan [Phys. Rev. E 69, 026113 (2004)], is modularity maximization. Many heuristics have been proposed for maximizing modularity and yield rapid...

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Veröffentlicht in:Physical review. E, Statistical, nonlinear, and soft matter physics Jg. 82; H. 4; S. 046112
Hauptverfasser: Aloise, Daniel, Cafieri, Sonia, Caporossi, Gilles, Hansen, Pierre, Perron, Sylvain, Liberti, Leo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States American Physical Society 01.10.2010
Schlagworte:
Mathematics
Optimization and Control
ISSN:1539-3755, 1550-2376, 1550-2376
Online-Zugang:Volltext
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Zusammenfassung:Finding modules, or clusters, in networks currently attracts much attention in several domains. The most studied criterion for doing so, due to Newman and Girvan [Phys. Rev. E 69, 026113 (2004)], is modularity maximization. Many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality. There are few exact algorithms, prominent among which is a paper by Xu [Eur. Phys. J. B 60, 231 (2007)]. Modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of Grötschel and Wakabayashi [Math. Program. 45, 59 (1989)] applied. We propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming. Performance of the four resulting algorithms is compared on problems from the literature. Instances with up to 512 entities are solved exactly. Moreover, the computing time of previously solved problems are reduced substantially.
Bibliographie:ObjectType-Article-1
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ISSN:1539-3755
1550-2376
1550-2376
DOI:10.1103/PhysRevE.82.046112