Geodesic
A note on tree realizations of matrices
RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 4, pp. 361-366

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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 m ij +m kl ≤max{m ik +m jl ,m il +m jk } for all distinct i,j,k,l.

DOI : 10.1051/ro:2007028
Classification : 05C50, 05B20, 68R10, 68U99
Keywords: matrices, tree metrics, 4-point condition 
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     author = {Hertz, Alain and Varone, Sacha},
     title = {A note on tree realizations of matrices},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {361--366},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {4},
     year = {2007},
     doi = {10.1051/ro:2007028},
     mrnumber = {2361290},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro:2007028/}
}
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Hertz, Alain; Varone, Sacha. A note on tree realizations of matrices. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 4, pp. 361-366. doi: 10.1051/ro:2007028

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