On the structure of the tight-span of a totally split-decomposable metric

Huber, K.T., Koolen, J. and Moulton, V. (2006) On the structure of the tight-span of a totally split-decomposable metric. European Journal of Combinatorics, 27 (3). pp. 461-479. ISSN 0195-6698

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Abstract

The tight-span of a finite metric space is a polytopal complex with a structure that reflects properties of the metric. In this paper we consider the tight-span of a totally split-decomposable metric. Such metrics are used in the field of phylogenetic analysis, and a better knowledge of the structure of their tight-spans should ultimately provide improved phylogenetic techniques. Here we prove that a totally split-decomposable metric is cell-decomposable. This allows us to break up the tight-span of a totally split-decomposable metric into smaller, easier to understand tight-spans. As a consequence we prove that the cells in the tight-span of a totally split-decomposable metric are zonotopes that are polytope isomorphic to either hypercubes or rhombic dodecahedra.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 23 May 2011 07:53
Last Modified: 21 Apr 2020 19:37
URI: https://ueaeprints.uea.ac.uk/id/eprint/21530
DOI: 10.1016/j.ejc.2004.05.007

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