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A note on tree realizations of matrices

Published online by Cambridge University Press:  11 October 2007

Alain Hertz  and
Sacha Varone
Alain Hertz
Affiliation:
Département de mathématiques et de génie industriel, École Polytechnique, Montréal, Canada; alain.hertz@gerad.ca
Sacha Varone
Affiliation:
Haute école de gestion de Genève, Économie d'Entreprise, Genève, Switzerland; sacha.varone@hesge.ch
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Abstract

It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i,j,k,l.

Keywords

Matricestree metrics4-point condition
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 4 , October 2007 , pp. 361 - 366
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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