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The triangles method to build X-trees from 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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References

Barthélemy J.P. and Guénoche A., Trees and proximities representations. J. Wiley, Chichester, UK (1991).
Buneman P., The recovery of trees from measures of dissimilarity, edited by F.R. Hodson, D.G. Kendall and P. Tautu, Mathematics in Archaeological and Historical Sciences. Edinburg University Press, Edinburg (1971) 387-395.
Duret, L., Mouchiroud, D. and Gouy, M., HOVERGEN: A database of homologous vertebrate genes. Nucleic Acids Res. 22 (1994) 2360-2365. CrossRef
Farris, J.S., Estimating phylogenetic trees from distance matrices. Amer. Nat. 106 (1972) 645-668. CrossRef
Gascuel, O., A note on Sattah and Tversky's, Saitou and Nei's and Studier and Keppler's algorithms for inferring phylogenies from evolutionary distances. Mol. Biol. Evol. 11 (1994) 961-963.
Gascuel, O., BIONJ: An improved version of the NJ algorithm based on a simple model of sequence data. Mol. Biol. Evol. 14 (1997) 685-695. CrossRef
Guénoche A., Order distances in tree reconstruction, edited by B. Mirkin et al., Mathematical Hierarchies and Biology. American Mathematical Society, Providence, RI, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 37 (1997) 171-182.
Guénoche, A. and S. Grandcolas S., Approximation par arbre d'une distance partielle. Math. Inform. Sci. Humaines 146 (1999) 51-64.
Harary, F. and Palmer, E.M., On acyclical simplicial complexes. Mathematika 15 (1968) 115-122. CrossRef
Hein, J.J., An optimal algorithm to reconstruct trees from additive distance data. Bull. Math. Biol. 51 (1989) 597-603. CrossRef
Lapointe, F.J. and Kirsch, J.A.W., Estimating phylogenies from lacunose distance matrices: Additive is superior to ultrametric estimation. Mol. Biol. Evol. 13 (1996) 266-284.
Leclerc, B., Minimum spanning trees for tree metrics: Abridgements and adjustments. J. Classification 12 (1995) 207-241. CrossRef
Leclerc, B. and Makarenkov, V., On some relations between 2-trees and tree metrics. Discrete Math. 192 (1998) 223-249. CrossRef
Makarenkov V., Propriétés combinatoires des distances d'arbre : algorithmes et applications. Thèse de l'EHESS, Paris (1997).
Pippert R.E. and Beineke L.W., Characterisation of 2-dimentional trees, edited by G. Chatrand and S.F. Kapoor, The Many Facets of Graph Theory. Springer-Verlag, Berlin, Lecture Notes in Math. 110 (1969) 263-270.
Prim, R.C., Shortest connection network and some generalizations. Bell System Tech. J. 26 (1957) 1389-1401. CrossRef
Proskurowski, A., Separating subgraphs in k-trees: Cables and caterpillars. Discrete Math. 49 (1984) 275-295. CrossRef
Robinson, D.R. and Foulds, L.R., Comparison of phylogenetic trees. Math. Biosci. 53 (1981) 131-147. CrossRef
Rose, D.J., On simple characterizations of k-trees. Discrete Math. 7 (1974) 317-322. CrossRef
Saitou, N. and Nei, M., The neighbor-joining method: A new method for reconstructing phylogenetic trees. Mol. Biol. Evol. 4 (1987) 406-425.
Todd, P., A k-tree generalization that characterizes consistency of dimensioned engineering drawings. SIAM J. Discete Math. 2 (1989) 255-261. CrossRef
Waterman, M.S., Smith, T.F., Singh, M. and Beyer, W.A., Additive Evolutionary Trees. J. Theor. Biol. 64 (1977) 199-213. CrossRef