Obtaining splits from cut sets of tight spans

A. Dress, Vincent Moulton, Taoyang Wu, A. Spillner

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

To any metric D on a finite set X, one can associate a metric space T(D) known as its tight span. Properties of T(D) often reveal salient properties of D. For example, cut sets of T(D), i.e., subsets of T(D) whose removal disconnect T(D), can help to identify clusters suggested by D and indicate how T(D) (and hence D) may be decomposed into simpler components. Given a bipartition or split S of X, we introduce in this paper a real-valued index e( that comes about by considering cut sets of T(D). We also show that this index is intimately related to another, more easily computable index d( whose definition does not directly depend on T(D). In addition, we provide an illustration for how these two new indices could help to extend and complement current distance-based methods for phylogenetic network construction such as split decomposition and NeighborNet.
Original languageEnglish
Pages (from-to)1409-1420
Number of pages12
JournalDiscrete Applied Mathematics
Volume161
Issue number10-11
DOIs
Publication statusPublished - 1 Jul 2013

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