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tree metrics

RAIRO - Operations Research (1)

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A note on tree realizations of matrices
Alain Hertz, Sacha Varone
Journal:

RAIRO - Operations Research / Volume 41 / Issue 4 / October 2007

Published online by Cambridge University Press:

11 October 2007, pp. 361-366

Print publication:

October 2007
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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.