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Journal of Classification

, Volume 27, Issue 2, pp 158–172 | Cite as

An Algorithm for Computing Cutpoints in Finite Metric Spaces

  • Andreas Dress
  • Katharina T. Huber
  • Jacobus Koolen
  • Vincent Moulton
  • Andreas Spillner
Article

Abstract

The theory of the tight span, a cell complex that can be associated to every metric D, offers a unifying view on existing approaches for analyzing distance data, in particular for decomposing a metric D into a sum of simpler metrics as well as for representing it by certain specific edge-weighted graphs, often referred to as realizations of D. Many of these approaches involve the explicit or implicit computation of the so-called cutpoints of (the tight span of) D, such as the algorithm for computing the “building blocks” of optimal realizations of D recently presented by A. Hertz and S. Varone. The main result of this paper is an algorithm for computing the set of these cutpoints for a metric D on a finite set with n elements in O(n3) time. As a direct consequence, this improves the run time of the aforementioned O(n6)-algorithm by Hertz and Varone by “three orders of magnitude”.

Keywords

Metric Cutpoint Realization Tight span Decomposition Block 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Andreas Dress
    • 1
  • Katharina T. Huber
    • 2
  • Jacobus Koolen
    • 3
  • Vincent Moulton
    • 2
  • Andreas Spillner
    • 4
  1. 1.CAS-MPG Partner Institute and Key Lab for Computational Biology (PICB)ShanghaiChina
  2. 2.University of East AngliaEast AngliaUK
  3. 3.Pohang Mathematics Institute and POSTECHPohang-siSouth Korea
  4. 4.University of GreifswaldDeutschlandGermany

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