A Characterization of Minimum Spanning Tree-Like Metric Spaces

Momoko Hayamizu, Hiroshi Endo, Kenji Fukumizu

Research output: Contribution to journalArticle

Abstract

Recent years have witnessed a surge of biological interest in the minimum spanning tree (MST) problem for its relevance to automatic model construction using the distances between data points. Despite the increasing use of MST algorithms for this purpose, the goodness-of-fit of an MST to the data is often elusive because no quantitative criteria have been developed to measure it. Motivated by this, we provide a necessary and sufficient condition to ensure that a metric space on $n$ points can be represented by a fully labeled tree on $n$ vertices, and thereby determine when an MST preserves all pairwise distances between points in a finite metric space.

Original languageEnglish
Article number7447693
Pages (from-to)468-471
Number of pages4
JournalIEEE/ACM Transactions on Computational Biology and Bioinformatics
Volume14
Issue number2
DOIs
Publication statusPublished - 2017 Mar 1
Externally publishedYes

Keywords

  • Cellular differentiation
  • distance-based tree estimation
  • four-point condition
  • fourth-point condition
  • minimum spanning tree

ASJC Scopus subject areas

  • Biotechnology
  • Genetics
  • Applied Mathematics

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