The triangles method to build X-trees from incomplete distance matrices
RAIRO - Operations Research - Recherche Opérationnelle, Volume 35 (2001) no. 2, pp. 283-300.

A method to infer X-trees (valued trees having X as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2n-3 distance values between the n elements of X, if they fulfill some explicit conditions. This construction is based on the mapping between X-tree and a weighted generalized 2-tree spanning X.

On décrit une méthode pour la reconstruction des X-arbres (arbres valués admettant X comme ensemble de feuilles) à partir de tableaux de distances incomplets (où certaines valeurs sont incertaines ou inconnues). Elle permet de construire un arbre non orienté à partir de 2n-3 valeurs de distance entre les n éléments de X, sous des conditions qui sont explicitées. Cette construction est basée sur une relation entre X-arbres et 2-arbres valués généralisés d’ensemble de sommets X.

Keywords: X-tree, partial distances, 2-trees
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     title = {The triangles method to build $X$-trees from incomplete distance matrices},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {283--300},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {2},
     year = {2001},
     mrnumber = {1868873},
     zbl = {0992.05036},
     language = {en},
     url = {http://www.numdam.org/item/RO_2001__35_2_283_0/}
}
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Guénoche, Alain; Leclerc, Bruno. The triangles method to build $X$-trees from incomplete distance matrices. RAIRO - Operations Research - Recherche Opérationnelle, Volume 35 (2001) no. 2, pp. 283-300. http://www.numdam.org/item/RO_2001__35_2_283_0/

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