Characterizing cell-decomposable metrics (Q1010659)

To each finite metric space \((X,d)\) is associated the so-called tight-span \(T(d)\) of \(d,\) that is, a canonical metric space \((T(d),d_\infty)\) into which \((X,d)\) isometrically embeds and which may be thought of as the abstract convex hull of \((X,d)\). To better understand the structure of \((T(d),d_\infty)\) the concept of a cell-decomposable metric was recently introduced as a kind of metric whose associated tight-span can be decomposed into simpler tight-spans. The authors show that cell-decomposable metrics and totally split-decomposable metrics -- a class of metrics commonly applied within phylogenetic analysis -- are one and the same thing, and also provide some additional characterizations of such metrics.