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The triangles method to build X-treesfrom incomplete distance matrices

Published online by Cambridge University Press:  15 August 2002

Alain Guénoche  and
Bruno Leclerc
Alain Guénoche
Affiliation:
Institut Mathématique de Luminy, CNRS, 163 avenue de Luminy, 13009 Marseille, France; guenoche@iml.univ-mrs.fr.
Bruno Leclerc
Affiliation:
Centre d'Analyse et de Mathématiques Sociales, École des Hautes Études en Sciences Sociales, 54 boulevard Raspail, 75270 Paris Cedex 06, France; leclerc@ehess.fr.
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Abstract

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.

Keywords

X-treepartial distances2-trees.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 2: ROADEF'99 , April 2001 , pp. 283 - 300
Copyright
© EDP Sciences, 2001

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