Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.dam.2013.02.001
Title: Obtaining splits from cut sets of tight spans
Authors: Dress, A.
Moulton, V.
Spillner, A.
Wu, T. 
Keywords: Cut set
Metric space
Phylogenetic network
Split index
Tight span
Issue Date: Jul-2013
Citation: Dress, A., Moulton, V., Spillner, A., Wu, T. (2013-07). Obtaining splits from cut sets of tight spans. Discrete Applied Mathematics 161 (10-11) : 1409-1420. ScholarBank@NUS Repository. https://doi.org/10.1016/j.dam.2013.02.001
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 ε(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 δ( 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. © © 2013 Elsevier B.V. All rights reserved.
Source Title: Discrete Applied Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103663
ISSN: 0166218X
DOI: 10.1016/j.dam.2013.02.001
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