A note on tree realizations of matrices

A note on tree realizations of matrices

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Article ID: iaor20083362
Country: France
Volume: 41
Issue: 4
Start Page Number: 361
End Page Number: 366
Publication Date: Oct 2007
Journal: RAIRO Operations Research
Authors: ,
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.

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