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A linear programming based heuristic for a hard clustering problem on trees

  • Isabella Lari
  • Maurizio Maravalle
  • Bruno Simeone
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Clustering problems with relational constraints in which the underlying graph is a tree arise in a variety of applications: hierarchical data base paging, communication and distribution network districting, biological taxonomy, and others. They are formulated here as optimal tree partitioning problems. In a previous paper, it was shown that their computational complexity strongly depends on the nature of the objective function and, in particular, that minimizing the total within-cluster dissimilarity or the diameter is computationally hard. We propose a heuristic which finds good partitions for the first problem within a reasonable time, even when its size is large. Such heuristic is based on the solution of a linear program and a maximal network flow one, and in any case it yields an explicit estimate of the relative approximation error. With minor variations a similar approach yields good solutions for the minimum diameter problem.

Key words

Contiguity-constrained clustering 

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Isabella Lari
    • 1
  • Maurizio Maravalle
    • 2
  • Bruno Simeone
    • 1
  1. 1.Department of Statistics“La Sapienza” UniversityRomeItaly
  2. 2.Department of Systems for EconomicsUniversity of L’AquilaL’AquilaItaly

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