A note on tree realizations of matrices

Hertz, Alain; Varone, Sacha

doi:10.1051/ro:2007028

Hertz, Alain ; Varone, Sacha

RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 4, pp. 361-366

Résumé

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 $m_{i j} + m_{k l} \leq m a x {m_{i k} + m_{j l}, m_{i l} + m_{j k}}$ for all distinct $i, j, k, l$ .

MR

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},
     year = {2007},
     publisher = {EDP Sciences},
     volume = {41},
     number = {4},
     doi = {10.1051/ro:2007028},
     mrnumber = {2361290},
     language = {en},
     url = {https://www.numdam.org/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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