An algorithm for computing cutpoints in finite metric spaces

AWM Dress, KT Huber, J Koolen, V Moulton, A Spillner

Research output: Contribution to journalArticle

9 Citations (Scopus)

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”.
Original languageEnglish
Pages (from-to)158-172
Number of pages15
JournalJournal of Classification
Volume27
Issue number2
DOIs
Publication statusPublished - 2010

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