The polytopal structure of the tight-span of a totally split-decomposable metric

Huber, Katharina, Koolen, Jack H. and Moulton, Vincent (2019) The polytopal structure of the tight-span of a totally split-decomposable metric. Discrete Mathematics, 342 (3). pp. 868-878. ISSN 0012-365X

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Abstract

The tight-span of a finite metric space is a polytopal complex that has appeared in several areas of mathematics. In this paper we determine the polytopal structure of the tight-span of a totally split-decomposable (finite) metric. These metrics are a generalization of tree-metrics and have importance within phylogenetics. In previous work, we showed that the cells of the tight-span of such a metric are zonotopes that are polytope isomorphic to either hypercubes or rhombic dodecahedra. Here, we extend these results and show that the tight-span of a totally split-decomposable metric can be broken up into a canonical collection of polytopal complexes whose polytopal structures can be directly determined from the metric. This allows us to also completely determine the polytopal structure of the tight-span of a totally split-decomposable metric. We anticipate that our improved understanding of this structure may lead to improved techniques for phylogenetic inference.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: LivePure Connector
Date Deposited: 01 Nov 2018 11:31
Last Modified: 27 Sep 2020 23:54
URI: https://ueaeprints.uea.ac.uk/id/eprint/68730
DOI: 10.1016/j.disc.2018.10.042

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