Advertisement

Linear-Time Algorithms for Two Subtree-Comparison Problems on Phylogenetic Trees with Different Species

  • Sun-Yuan Hsieh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4337)

Abstract

Phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time, in particular molecular sequences. In this paper, we consider two subtree-comparison problems on phylogenetic trees. Given a set of k phylogenetic trees whose leaves are drawn from {1,2,...,n} and the leaves for two arbitrary trees are not necessary the same, we first present a linear-time algorithm to final all maximal leaf-agreement subtrees. Based on this result, we also present a linear time algorithm to find maximal all-agreement isomorphic subtrees.

Keywords

Phylogenetic Tree Rooted Tree SIAM Journal Critical Node Auxiliary 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amir, A., Keselman, D.: Maximum agreement subtree in a set of evolutionary trees: Metrics and efficient algorithms. SIAM Journal on Computing 26(6), 1656–1669 (1997)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bonizzoni, P., Della Vedova, G., Mauri, G.: Approximating the maximum isomorphic agreement subtree is hard. In: Giancarlo, R., Sankoff, D. (eds.) CPM 2000. LNCS, vol. 1848, pp. 119–128. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Bryant, D.: Building Trees, Hunting for Trees, and Comparing Trees, PhD thesis, University of Canterbury, Christchurch, New Zealand (1997)Google Scholar
  4. 4.
    Cole, R., Farach, M., Hariharan, R., Przytycka, T., Thorup, M.: An O(nlogn) algorithm for the maximum agreement subtree problem for binary trees. SIAM Journal on Computing 30(5), 1385–1404 (2002)CrossRefGoogle Scholar
  5. 5.
    Day, W.H.E.: Optimal algorithms for comparing trees with labelled leaves. Journal of Classification 2, 7–28 (1985)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Farach, M., Przytycka, T.M., Thorup, M.: On the agreement of many trees. Information Processing Letters 55(6), 297–301 (1995)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Farach, M., Thorup, M.: Sparse dynamic programming for evolutionary-tree comparison. SIAM Journal on Computing 26(1), 210–230 (1997)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Felsenstein, J.: Numerical methods for inferring evolutionary trees. Quarterly Review on Biology 57(4), 379–404 (1982)CrossRefGoogle Scholar
  9. 9.
    Fitch, W.M.: Toward defining the course of evolution: minimal change for a specific tree topology. Systematic Zoology 20, 406–441 (1971)CrossRefGoogle Scholar
  10. 10.
    Gordon, A.D.: On the assessment and comparison of classifications. In: Tomassone, R. (ed.) Analyse de Données et Informatique, INRIA, pp. 149–160 (1980)Google Scholar
  11. 11.
    Gusfield, D.: Efficient algorithms for inferring evolutionary trees. Networks 21, 19–28 (1991)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Harel, D., Tarjan, R.E.: Fast algorithms for finding nearest common ancestors. SIAM Journal on Computing 13(2), 338–355 (1984)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hartigan, J.A.: Clustering Algorithms. John Wiley, Chichester (1975)MATHGoogle Scholar
  14. 14.
    Hein, J., Jiang, T., Wang, L., Zhang, K.: On the complexity of comparing evolutionary trees. Discrete Applied Mathematics 71, 153–169 (1996)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Hoch, J.A., Silhavy, T.J.: Two-Component Signal Transduction. ASM Press, Washington (1995)Google Scholar
  16. 16.
    Lin, Y.L., Hsu, T.S.: Efficient algorithms for descendent subtrees comparison of phylogenetic trees with applications to co-evolutionary classifications in bacterial genome. In: Proceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC). LNCS, vol. 2906, pp. 339–351. Springer, Heidelberg (2003)Google Scholar
  17. 17.
    Rodrigue, A., Quentin, Y., Lazdunski, A., M/’ejean, V., Foglino, M.: Two-component systems in pseudomonas aeruginosa: why so many? Trends Microbiol. 8, 498–504 (2000)CrossRefGoogle Scholar
  18. 18.
    Saitou, N., Nei, M.: The neighbor-joining method: a new method for reconstructing phylogenetic trees. Molecular Biology Evolution 4, 406–425 (1987)Google Scholar
  19. 19.
    Setubal, J.C., Meidanis, J.: Introduction to Computational Molecular Biology. PWS Publishing company (1997)Google Scholar
  20. 20.
    Strimmer, K., von Haeseler, A.: Quartet puzzling: a quartet maximum-likelihood method for reconstructing tree topologies. Molecular Biology and Evolution 13(7), 964–969 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sun-Yuan Hsieh
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Cheng Kung UniversityTainanTaiwan

Personalised recommendations