Tropical Fermat--Weber Points

DOI10.1137/16M1071122zbMath1420.14148arXiv1604.04674MaRDI QIDQ4564885

Ruriko Yoshida, Bo Lin

Publication date: 7 June 2018

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

Full work available at URL: https://arxiv.org/abs/1604.04674

zbMATH Keywords

convex polytopestropical geometryultrametricsFermat-Weber points

Mathematics Subject Classification ID

Related Items (10)

Tropical optimal transport and Wasserstein distances ⋮ Information geometry for phylogenetic trees ⋮ Tropical geometric variation of tree shapes ⋮ L-Infinity Optimization to Linear Spaces and Phylogenetic Trees ⋮ Tropical medians by transportation ⋮ Convexity in Tree Spaces ⋮ Classifying tree topology changes along tropical line segments ⋮ Asymmetric tropical distances and power diagrams ⋮ Tropical principal component analysis and its application to phylogenetics ⋮ L-Infinity Optimization to Bergman Fans of Matroids with an Application to Phylogenetics

Uses Software

• Maple
• polymake
• ape

Cites Work

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• Best approximation in max-plus semimodules
• Duality and separation theorems in idempotent semimodules.
• Geometry of the space of phylogenetic trees
• Shortest connectivity. An introduction with applications in phylogeny.
• Lectures on Polytopes
• The tropical Grassmannian
• L-Infinity Optimization to Linear Spaces and Phylogenetic Trees
• Convexity in Tree Spaces

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