Characterizing Cell-Decomposable Metrics

Characterizing Cell-Decomposable Metrics

To a finite metric space (X, d) one can associate the so called tight-span T (d) of d, that is, a canonical metric space (T (d), d∞) into which (X, d) isometrically embeds and which may be thought of as the abstract convex hull of (X, d). Amongst other applications, the tight-span of a finite metric space has been used to decompose and classify finite metrics, to solve instances of the server a...

Structure and Applications of Totally Decomposable Metrics

On Decomposable Measures Induced by Metrics

A Note on Circular Decomposable Metrics

A metric d on a finite set X is called a Kalmanson metric if there exists a circular ordering of points of X , such that d(y; u) + d(z; v) > d(y; z) + d(u; v) for all crossing pairs yu and zv of . We prove that any Kalmanson metric d is an l1-metric, i.e. d can be written as a nonnegative linear combination of split metrics. The splits in the decomposition of d can be selected to form a circula...

The Structure of Circular Decomposable Metrics