Convexity in Tree Spaces

DOI10.1137/16M1079841zbMath1370.05040arXiv1510.08797MaRDI QIDQ5357960

Ruriko Yoshida, Bernd Sturmfels, Xiaoxian Tang, Bo Lin

Publication date: 18 September 2017

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08797

zbMATH Keywords

CAT(0) spacepolytopegeodesic trianglephylogenetic treeultrametrictropical convexityBillera-Holmes-Vogtman metric

Mathematics Subject Classification ID

Trees (05C05) Problems related to evolution (92D15) Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) General convexity (52A99)

Related Items

Tree topologies along a tropical line segment, Tropical optimal transport and Wasserstein distances, Tropical Fermat--Weber Points, Tropical geometric variation of tree shapes, L-Infinity Optimization to Linear Spaces and Phylogenetic Trees, Old and new challenges in Hadamard spaces, Tropical Linear Regression and Mean Payoff Games: Or, How to Measure the Distance to Equilibria, Plücker coordinates of the best-fit Stiefel tropical linear space to a mixture of Gaussian distributions, Tropical medians by transportation, A Space of Phylogenetic Networks, Shortest paths and convex hulls in 2D complexes with non-positive curvature, Tropical principal component analysis and its application to phylogenetics, New Gromov-inspired metrics on phylogenetic tree space, L-Infinity Optimization to Bergman Fans of Matroids with an Application to Phylogenetics

Uses Software

• polymake
• ape

Cites Work

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