The triangles method to build X-trees from incomplete distance matrices

Alain Guénoche; Bruno Leclerc

RAIRO - Operations Research (2010)

  • Volume: 35, Issue: 2, page 283-300
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Guénoche, Alain, and Leclerc, Bruno. "The triangles method to build X-trees from incomplete distance matrices." RAIRO - Operations Research 35.2 (2010): 283-300. <http://eudml.org/doc/116595>.

@article{Guénoche2010,
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. },
author = {Guénoche, Alain, Leclerc, Bruno},
journal = {RAIRO - Operations Research},
keywords = {X-tree; partial distances; 2-trees.; valued trees; distance arrays; twotree; spanning tree},
language = {eng},
month = {3},
number = {2},
pages = {283-300},
publisher = {EDP Sciences},
title = {The triangles method to build X-trees from incomplete distance matrices},
url = {http://eudml.org/doc/116595},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Guénoche, Alain
AU - Leclerc, Bruno
TI - The triangles method to build X-trees from incomplete distance matrices
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 2
SP - 283
EP - 300
AB - 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.
LA - eng
KW - X-tree; partial distances; 2-trees.; valued trees; distance arrays; twotree; spanning tree
UR - http://eudml.org/doc/116595
ER -

References

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  1. Barthélemy J.P. and Guénoche A., Trees and proximities representations. J. Wiley, Chichester, UK (1991).  Zbl0790.05021
  2. 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.  
  3. Duret L., Mouchiroud D. and Gouy M., HOVERGEN: A database of homologous vertebrate genes. Nucleic Acids Res.22 (1994) 2360-2365.  
  4. Farris J.S., Estimating phylogenetic trees from distance matrices. Amer. Nat.106 (1972) 645-668.  
  5. 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.  
  6. 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.  
  7. 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.  Zbl0886.05051
  8. Guénoche A. and S. Grandcolas S., Approximation par arbre d'une distance partielle. Math. Inform. Sci. Humaines146 (1999) 51-64.  
  9. Harary F. and Palmer E.M., On acyclical simplicial complexes. Mathematika15 (1968) 115-122.  Zbl0157.54903
  10. Hein J.J., An optimal algorithm to reconstruct trees from additive distance data. Bull. Math. Biol.51 (1989) 597-603.  Zbl0674.92003
  11. 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.  
  12. Leclerc B., Minimum spanning trees for tree metrics: Abridgements and adjustments. J. Classification12 (1995) 207-241.  Zbl0845.62046
  13. Leclerc B. and Makarenkov V., On some relations between 2-trees and tree metrics. Discrete Math.192 (1998) 223-249.  Zbl0958.05029
  14. Makarenkov V., Propriétés combinatoires des distances d'arbre : algorithmes et applications. Thèse de l'EHESS, Paris (1997).  
  15. 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.  
  16. Prim R.C., Shortest connection network and some generalizations. Bell System Tech. J.26 (1957) 1389-1401.  
  17. Proskurowski A., Separating subgraphs in k-trees: Cables and caterpillars. Discrete Math.49 (1984) 275-295.  Zbl0543.05041
  18. Robinson D.R. and Foulds L.R., Comparison of phylogenetic trees. Math. Biosci.53 (1981) 131-147.  Zbl0451.92006
  19. Rose D.J., On simple characterizations of k-trees. Discrete Math.7 (1974) 317-322.  Zbl0285.05128
  20. Saitou N. and Nei M., The neighbor-joining method: A new method for reconstructing phylogenetic trees. Mol. Biol. Evol.4 (1987) 406-425.  
  21. Todd P., A k-tree generalization that characterizes consistency of dimensioned engineering drawings. SIAM J. Discete Math.2 (1989) 255-261.  Zbl0684.05017
  22. Waterman M.S., Smith T.F., Singh M. and Beyer W.A., Additive Evolutionary Trees. J. Theor. Biol.64 (1977) 199-213.  

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