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Mathematical Programming

, Volume 74, Issue 3, pp 247–266 | Cite as

Formulations and valid inequalities for the node capacitated graph partitioning problem

  • C. E. Ferreira
  • A. Martin
  • C. C. de Souza
  • R. Weismantel
  • L. A. Wolsey
Article

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.

Keywords

Clustering Graph partitioning Equipartition Knapsack Integer programming Ear decomposition 

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Copyright information

© The Mathematical Programming Society. Inc. 1996

Authors and Affiliations

  • C. E. Ferreira
    • 1
  • A. Martin
    • 2
  • C. C. de Souza
    • 3
  • R. Weismantel
    • 2
  • L. A. Wolsey
    • 4
  1. 1.Universidade de São PauloSão PauloBrazil
  2. 2.Konrad-Zuse-Zentrum für InformationstechnikBerlinGermany
  3. 3.Universidade Estadual de CampinasBrazil
  4. 4.COREUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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