Groupe d’études et de recherche en analyse des décisions

G-2005-27

A Note on Tree Realizations of Matrices

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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.

, 8 pages