Abstract:
The study of cohesive subgroups is an important aspect of social network analysis. Cohesive subgroups are studied using different relaxations of the notion of clique in a graph. For instance, given a graph and an integer k, the maximum edge subgraph problem consists of finding a k-vertex subset such that the number of edges within the subset is maximum. This work proposes a polyhedral approach for this NP-hard problem. We study the polytope associated to an integer programming formulation of the problem, present several families of facet-inducing valid inequalities, and discuss the separation problem associated to these families. Finally, we implement a branch and cut algorithm for this problem. This computational study illustrates the effectiveness of the classes of inequalities presented in this work. © 2011 Elsevier B.V. All rights reserved.
Registro:
Documento: |
Artículo
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Título: | A polyhedral study of the maximum edge subgraph problem |
Autor: | Bonomo, F.; Marenco, J.; Saban, D.; Stier-Moses, N.E. |
Filiación: | Depto. de Computación, FCEyN, IMAS-CONICET, Argentina Instituto de Ciencias, Universidad Nacional de General Sarmiento, Argentina Depto. de Computación, FCEyN, Universidad de Buenos Aires, Argentina Graduate School of Business, Columbia University, United States
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Palabras clave: | Maximum edge subgraph problem; Polyhedral combinatorics; Quasi-cliques; Branch-and-cut algorithms; Computational studies; Integer programming formulations; Polyhedral approach; Polyhedral combinatorics; Polyhedral studies; Polytopes; Quasi-cliques; Separation problems; Social Network Analysis; Subgraph problems; Valid inequality; Integer programming; Linear programming; Social networking (online); Computational complexity |
Año: | 2012
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Volumen: | 160
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Número: | 18
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Página de inicio: | 2573
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Página de fin: | 2590
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DOI: |
http://dx.doi.org/10.1016/j.dam.2011.10.011 |
Título revista: | Discrete Applied Mathematics
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Título revista abreviado: | Discrete Appl Math
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ISSN: | 0166218X
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CODEN: | DAMAD
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PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0166218X_v160_n18_p2573_Bonomo.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v160_n18_p2573_Bonomo |
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Citas:
---------- APA ----------
Bonomo, F., Marenco, J., Saban, D. & Stier-Moses, N.E.
(2012)
. A polyhedral study of the maximum edge subgraph problem. Discrete Applied Mathematics, 160(18), 2573-2590.
http://dx.doi.org/10.1016/j.dam.2011.10.011---------- CHICAGO ----------
Bonomo, F., Marenco, J., Saban, D., Stier-Moses, N.E.
"A polyhedral study of the maximum edge subgraph problem"
. Discrete Applied Mathematics 160, no. 18
(2012) : 2573-2590.
http://dx.doi.org/10.1016/j.dam.2011.10.011---------- MLA ----------
Bonomo, F., Marenco, J., Saban, D., Stier-Moses, N.E.
"A polyhedral study of the maximum edge subgraph problem"
. Discrete Applied Mathematics, vol. 160, no. 18, 2012, pp. 2573-2590.
http://dx.doi.org/10.1016/j.dam.2011.10.011---------- VANCOUVER ----------
Bonomo, F., Marenco, J., Saban, D., Stier-Moses, N.E. A polyhedral study of the maximum edge subgraph problem. Discrete Appl Math. 2012;160(18):2573-2590.
http://dx.doi.org/10.1016/j.dam.2011.10.011