A note on \(M\)-convexity in polyhedral split decomposition of distances

DOI10.1007/s13160-011-0052-yzbMath1260.52008OpenAlexW2140175100MaRDI QIDQ691985

Shungo Koichi

Publication date: 4 December 2012

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-011-0052-y

zbMATH Keywords

tree metric\(M\)-convex functioncross-free familypolyhedral split decompositionsplit-decomposability

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Convex functions and convex programs in convex geometry (52A41)

Cites Work

• A canonical decomposition theory for metrics on a finite set
• \(M\)-convex functions and tree metrics
• Extension of M-convexity and L-convexity to polyhedral convex functions
• A geometric study of the split decomposition
• Analytic inversion of the five-point Poisson operator
• Submodular functions and optimization.
• Basic Phylogenetic Combinatorics
• Discrete Convex Analysis

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