Mathematical Programming

, Volume 45, Issue 1–3, pp 59–96

A cutting plane algorithm for a clustering problem

  • M. Grötschel
  • Y. Wakabayashi


In this paper we consider a clustering problem that arises in qualitative data analysis. This problem can be transformed to a combinatorial optimization problem, the clique partitioning problem. We have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope. These theoretical results are utilized in this paper. We describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before. We discuss some details of the implementation of our code and present our computational results. We mention applications from, e.g., zoology, economics, and the political sciences.


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Copyright information

© North-Holland 1989

Authors and Affiliations

  • M. Grötschel
    • 1
  • Y. Wakabayashi
    • 2
  1. 1.Institut für MathematikUniversität AugsburgAugsburgWest Germany
  2. 2.Instituto de Mathemática e EstatísticaUniversidade de São PauloSão PauloBrazil

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