Issue |
RAIRO-Oper. Res.
Volume 41, Number 4, October-December 2007
|
|
---|---|---|
Page(s) | 361 - 366 | |
DOI | https://doi.org/10.1051/ro:2007028 | |
Published online | 11 October 2007 |
A note on tree realizations of matrices
1
Département de mathématiques et de génie industriel, École Polytechnique, Montréal, Canada; alain.hertz@gerad.ca
2
Haute école de gestion de Genève, Économie d'Entreprise, Genève, Switzerland; sacha.varone@hesge.ch
Received:
7
March
2005
Accepted:
19
January
2007
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.
Mathematics Subject Classification: 05C50 / 05B20 / 68R10 / 68U99
Key words: Matrices / tree metrics / 4-point condition
© EDP Sciences, ROADEF, SMAI, 2007
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