CONVEXITY IN TREE SPACES

被引：27
|
作者：
Lin, Bo [1 ]
Sturmfels, Bernd [1 ]
Tang, Xiaoxian [2 ]
Yoshida, Ruriko [3 ]
机构：
[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
[3] Naval Postgrad Sch, Dept Operat Res, Monterey, CA 93940 USA
来源：
SIAM JOURNAL ON DISCRETE MATHEMATICS | 2017年 / 31卷 / 03期
基金：
美国国家科学基金会;
关键词：
Billera-Holmes-Vogtman metric; ultrametric; CAT(0) space; geodesic triangle; phylogenetic tree; polytope; tropical convexity; GEOMETRY; APPROXIMATION; ALGORITHM;
D O I：
10.1137/16M1079841
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：2015 / 2038
页数：24
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