Computing the Quartet Distance Between Trees of Arbitrary Degree

  • Chris Christiansen
  • Thomas Mailund
  • Christian N. S. Pedersen
  • Martin Randers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3692)


We present two algorithms for computing the quartet distance between trees of arbitrary degree. The quartet distance between two unrooted evolutionary trees is the number of quartets—sub-trees induced by four leaves—that differs between the trees. Previous algorithms focus on computing the quartet distance between binary trees. In this paper, we present two algorithms for computing the quartet distance between trees of arbitrary degrees. One in time O(n 3) and space O(n 2) and one in time O(n 2 d 2) and space O(n 2), where n is the number of species and d is the maximal degree of the internal nodes of the trees. We experimentally compare the two algorithms and discuss possible directions for improving the running time further.


Binary Tree Internal Node Directed Edge Extended Tree Original Tree 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Allen, B.L., Steel, M.: Subtree transfer operations and their induced metrics on evolutionary trees. Annals of Combinatorics 5, 1–13 (2001)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Berry, V., Bryant, D.: Faster reliable phylogenetic analysis. In: Proc. 3rd International Conference on Computational Molecular Biology, RECOMB (1999)Google Scholar
  3. 3.
    Brodal, G.S., Fagerberg, R., Pedersen, C.N.S.: Computing the quartet distance between evolutionary trees in time O(n logn). Algorithmica 38, 377–395 (2003)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Bryant, D., Moulton, V.: A polynomial time algorithm for constructing the refined buneman tree. Applied Mathematics Letters 12, 51–56 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bryant, D., Tsang, J., Kearney, P.E., Li, M.: Computing the quartet distance between evolutionary trees. In: Proceedings of the 11th Annual Symposium on Discrete Algorithms (SODA), pp. 285–286 (2000)Google Scholar
  6. 6.
    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
  7. 7.
    Estabrook, G., McMorris, F., Meacham, C.: Comparison of undirected phylogenetic trees based on subtrees of four evolutionary units. Syst. Zool. 34, 193–200 (1985)CrossRefGoogle Scholar
  8. 8.
    Felsenstein, J.: Inferring Phylogenies. Sinauer Associates Inc. (2004)Google Scholar
  9. 9.
    Moulton, V., Steel, M.: Retractions of finite distance functions onto tree metrics. Discrete Applied Mathematics 91, 215–233 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Robinson, D.F., Foulds, L.R.: Comparison of weighted labelled trees. In: Combinatorial mathematics, VI (Proc. 6th Austral. Conf). Lecture Notes in Mathematics, pp. 119–126. Springer, Heidelberg (1979)CrossRefGoogle Scholar
  11. 11.
    Robinson, D.F., Foulds, L.R.: Comparison of phylogenetic trees. Mathematical Biosciences 53, 131–147 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Steel, M., Penny, D.: Distribution of tree comparison metrics–some new results. Syst. Biol. 42(2), 126–141 (1993)MathSciNetGoogle Scholar
  13. 13.
    Waterman, M.S., Smith, T.F.: On the similarity of dendrograms. Journal of Theoretical Biology 73, 789–800 (1978)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Chris Christiansen
    • 1
  • Thomas Mailund
    • 2
  • Christian N. S. Pedersen
    • 1
    • 2
  • Martin Randers
    • 1
  1. 1.Department of Computer ScienceUniversity of AarhusÅrhus NDenmark
  2. 2.Bioinformatics Research CenterUniversity of AarhusÅrhus CDenmark

Personalised recommendations