Obtaining splits from cut sets of tight spans

  • Authors:

  • Andreas Dress;Vincent Moulton;Andreas Spillner;Taoyang Wu

  • Affiliations:

  • CAS-MPG Partner Institute for Computational Biology (PICB), Shanghai Institutes for Biological Sciences (SIBS), Chinese Academy of Sciences (CAS), 320 Yue Yang Road, Shanghai 200031, PR China;School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK;Department of Mathematics and Computer Science, University of Greifswald, Greifswald, Germany;School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK and Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge, Singapore 119076, Singapore

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2013

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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"("D","S") 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"("D","S") 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.