TY - JOUR

T1 - Obtaining splits from cut sets of tight spans

AU - Dress, A.

AU - Moulton, Vincent

AU - Wu, Taoyang

AU - Spillner, A.

PY - 2013/7/1

Y1 - 2013/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84876419464&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2013.02.001

DO - 10.1016/j.dam.2013.02.001

M3 - Article

AN - SCOPUS:84876419464

VL - 161

SP - 1409

EP - 1420

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 10-11

ER -