# A note on tree realizations of matrices

RAIRO - Operations Research (2007)

- Volume: 41, Issue: 4, page 361-366
- ISSN: 0399-0559

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topHertz, Alain, and Varone, Sacha. "A note on tree realizations of matrices." RAIRO - Operations Research 41.4 (2007): 361-366. <http://eudml.org/doc/250136>.

@article{Hertz2007,

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.
},

author = {Hertz, Alain, Varone, Sacha},

journal = {RAIRO - Operations Research},

keywords = {Matrices; tree metrics; 4-point condition; matrices},

language = {eng},

month = {10},

number = {4},

pages = {361-366},

publisher = {EDP Sciences},

title = {A note on tree realizations of matrices},

url = {http://eudml.org/doc/250136},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Hertz, Alain

AU - Varone, Sacha

TI - A note on tree realizations of matrices

JO - RAIRO - Operations Research

DA - 2007/10//

PB - EDP Sciences

VL - 41

IS - 4

SP - 361

EP - 366

AB -
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.

LA - eng

KW - Matrices; tree metrics; 4-point condition; matrices

UR - http://eudml.org/doc/250136

ER -

## References

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