Convexity in Tree Spaces
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Authors
Lin, Bo
Sturmfels, Bernd
Tang, Xiaoxian
Yoshida, Ruriko
Subjects
Billera–Holmes–Vogtman metric
ultrametric
CAT(0) space
geodesic triangle
phylogenetic tree
polytope
tropical convexity
ultrametric
CAT(0) space
geodesic triangle
phylogenetic tree
polytope
tropical convexity
Advisors
Date of Issue
2017
Date
Publisher
Society for Industrial and Applied Mathematics (SIAM)
Language
Abstract
We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all ultrametrics. The CAT(0) metric of Billera–Holmes–Vogtman arises from the theory of orthant spaces. While its geodesics can be computed by the Owen–Provan algorithm, geodesic triangles are complicated. We show that the dimension of such a triangle can be arbitrarily high. Tropical convexity and the tropical metric exhibit properties that are desirable for geometric statistics, such as geodesics of small depth.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1137/16M1079841
Series/Report No
Department
Operations Research (OR)
Organization
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NPS Report Number
Sponsors
Funder
Format
Citation
Lin, Bo, et al. "Convexity in tree spaces." SIAM Journal on Discrete Mathematics 31.3 (2017): 2015-2038.
Distribution Statement
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.