Formulations and valid inequalities for the node capacitated graph partitioning problem |
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Authors: | C E Ferreira A Martin C C de Souza R Weismantel L A Wolsey |
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Institution: | 1. Universidade de S?o Paulo, S?o Paulo, Brazil 2. Konrad-Zuse-Zentrum für Informationstechnik, Berlin, Germany 3. Universidade Estadual de Campinas, Brazil 4. CORE, Université Catholique de Louvain, 1348, Louvain-la-Neuve, Belgium
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Abstract: | We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights
in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the
partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present
alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen
to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts.
In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem
parameters change. |
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Keywords: | Clustering Graph partitioning Equipartition Knapsack Integer programming Ear decomposition |
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