Journal of Classification

, Volume 4, Issue 2, pp 215–226

Minimum sum of diameters clustering

  • P. Hansen
  • B. Jaumard
Authors Of Articles

DOI: 10.1007/BF01896987

Cite this article as:
Hansen, P. & Jaumard, B. Journal of Classification (1987) 4: 215. doi:10.1007/BF01896987

Abstract

The problem of determining a partition of a given set ofN entities intoM clusters such that the sum of the diameters of these clusters is minimum has been studied by Brucker (1978). He proved that it is NP-complete forM≥3 and mentioned that its complexity was unknown forM=2. We provide anO(N3 logN) algorithm for this latter case. Moreover, we show that determining a partition into two clusters which minimizes any given function of the diameters can be done inO(N5) time.

Keywords

Partition Diameter Complexity Polynomial algorithm Divisive hierarchical clustering 

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • P. Hansen
    • 1
  • B. Jaumard
    • 2
  1. 1.Rutgers Center for Operations ResearchRutgers UniversityNew BrunswickUSA
  2. 2.Computer Aids for Industrial Productivity, Hill Center for the Mathematical SciencesRutgers UniversityNew BrunswickUSA

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