Advertisement

Computing Refined Buneman Trees in Cubic Time

  • Gerth Stølting Brodal
  • Rolf Fagerberg
  • Anna Östlin
  • Christian N. S. Pedersen
  • S. Srinivasa Rao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2812)

Abstract

Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics. Neighbor joining is a popular distance based tree reconstruction method. It always proposes fully resolved binary trees despite missing evidence in the underlying distance data. Distance based methods based on the theory of Buneman trees and refined Buneman trees avoid this problem by only proposing evolutionary trees whose edges satisfy a number of constraints. These trees might not be fully resolved but there is strong combinatorial evidence for each proposed edge. The currently best algorithm for computing the refined Buneman tree from a given distance measure has a running time of O(n 5) and a space consumption of O(n 4). In this paper, we present an algorithm with running time O(n 3) and space consumption O(n 2). The improved complexity of our algorithm makes the method of refined Buneman trees computational competitive to methods based on neighbor joining.

Keywords

Binary Tree Evolutionary Tree Dissimilarity Measure Space Usage Central Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bandelt, H.-J., Dress, A.W.: Reconstructing the shape of a tree from observed dissimilarity data. Advances in Applied Mathematics 7, 309–343 (1986)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Barthélémy, J.-P., Guénoche, A.: Trees and Proximity Representations. John Wiley & Sons, Chichester (1991)MATHGoogle Scholar
  3. 3.
    Berry, V., Bryant, D.: Faster reliable phylogenetic analysis. In: Proc. 3rd International Conference on Computational Molecular Biology (RECOMB), pp. 69–69 (1999)Google Scholar
  4. 4.
    Berry, V., Gascuel, O.: Inferring evolutionary trees with strong combinatorial evidence. Theoretical Computer Science 240, 271–298 (2000)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bryant, D., Berry, V.: A structured family of clustering and tree construction methods. Advances in Applied Mathematics 27(4), 705–732 (2001)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bryant, D., Moulton, V.: A polynomial time algorithm for constructing the refined buneman tree. Applied Mathematics Letters 12, 51–56 (1999)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Buneman, P.: The recovery of trees from measures of dissimilarity. In: Hodson, F., Kendall, D., Tautu, P. (eds.) Mathematics in Archaeological and Historical Sciences, pp. 387–395. Edinburgh University Press, Edinburgh (1971)Google Scholar
  8. 8.
    Gower, J.C., Ross, J.G.S.: Minimum spanning trees and single-linkage cluster analysis. Applied Statistics 18, 54–64 (1969)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Gusfield, D.: Efficient algorithms for inferring evolutionary trees. Networks 21, 19–28 (1991)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Huson, D.: Splitstree: a program for analyzing and visualizing evolutionary data. Bioinformatics 14(1), 68–73 (1998), http://www-ab.informatik.uni-tuebingen.de/software/splits/welcome_en.html CrossRefGoogle Scholar
  11. 11.
    Leclerc, B.: Description combinatoire des altramétriqueès. Math. Sci. Hum. 73, 5–37 (1981)MathSciNetGoogle Scholar
  12. 12.
    Moulton, V., Steel, M.: Retractions of finite distance functions onto tree metrics. Discrete Applied Mathematics 91, 215–233 (1999)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Nei, M., Kumar, S.: Molecular Evolution and Phylogenetics. Oxford University Press, Oxford (2000)Google Scholar
  14. 14.
    Saitou, N., Nei, M.: The neighbor-joining method: A new method for reconstructing phylogenetic trees. Molecular Biology Evolution 4, 406–425 (1987)Google Scholar
  15. 15.
    Schönhage, A., Paterson, M.S., Pippenger, N.: Finding the median. Journal of Computer and System Sciences 13, 184–199 (1976)MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Rolf Fagerberg
    • 1
  • Anna Östlin
    • 2
  • Christian N. S. Pedersen
    • 3
  • S. Srinivasa Rao
    • 4
  1. 1.BRICS (Basic Research in Computer Science), Department of Computer ScienceUniversity of AarhusÅrhus CDenmark
  2. 2.IT University of CopenhagenCopenhagen NV.
  3. 3.Bioinformatics Research Center (BiRC), Department of Computer ScienceUniversity of AarhusÅrhus CDenmark
  4. 4.School of Computer ScienceUniversity of WaterlooWaterloo

Personalised recommendations