Formulations and valid inequalities for the node capacitated graph partitioning problem

Formulations and valid inequalities for the node capacitated graph partitioning problem

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Article ID: iaor1998394
Country: Netherlands
Volume: 74
Issue: 3
Start Page Number: 247
End Page Number: 266
Publication Date: Sep 1996
Journal: Mathematical Programming
Authors: , , , ,
Keywords: graphs
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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