Optimal realizations and the block decomposition of a finite metric space

DOI10.1016/j.dam.2021.06.010zbMath1470.05072OpenAlexW3179298878MaRDI QIDQ2043363

Andreas Spillner, Katharina T. Huber, Vincent L. Moulton

Publication date: 2 August 2021

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2021.06.010

zbMATH Keywords

block decompositionfinite metric spacecut pointsoptimal realizationblock realization

Mathematics Subject Classification ID

Graph theory (including graph drawing) in computer science (68R10) Metric spaces, metrizability (54E35) Signed and weighted graphs (05C22)

Cites Work

• Unnamed Item
• An algorithm for computing cutpoints in finite metric spaces
• The metric cutpoint partition problem
• On optimal embeddings of metrics in graphs
• Block realizations of finite metrics and the tight-span construction. I: The embedding theorem
• Cut points in metric spaces
• Compatible decompositions and block realizations of finite metrics
• The metric bridge partition problem: Partitioning of a metric space into two subspaces linked by an edge in any optimal realization
• Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces
• On optimal realizations of finite metric spaces by graphs
• A canonical decomposition theory for metrics on a finite set
• Distance realization problems with applications to internet tomography
• The polytopal structure of the tight-span of a totally split-decomposable metric
• Searching for realizations of finite metric spaces in tight spans
• Towards a classification of transitive group actions on finite metric spaces
• \(T\)-theory: An overview
• Approximating minimum Manhattan networks in higher dimensions
• The Complexity of Metric Realization
• Distance matrix of a graph and its realizability

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