Skip to main content
SpringerLink
Log in

Tree contractions and evolutionary trees

  • Regular Presentations
  • Conference paper
  • First Online:
Algorithms and Complexity (CIAC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1203))

Included in the following conference series:

Abstract

An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of species. An agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees. We give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees T 1 and T 2 with n leaves each. If the maximum degree d of these trees is bounded by a constant, the time complexity is O(n log2 n) and is within a log n factor of optimal. For general d, this algorithm runs in O(nd 2 log d log2 n) time or alternatively in O(nd√d log3 n) time.

Supported in part by NSF Grant CCR-9101385.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. V. Aho, D. S. Hirschberg, and J. D. Ullman. Bounds on the complexity of the longest common subsequence problem. Journal of the ACM, 23(1):1–12, January 1976.

    Google Scholar 

  2. A. Apostolico and C. Guerra. The longest common subsequence problem revisited. Algorithmica, 2:315–336, 1987.

    Google Scholar 

  3. H. L. Bodlaender, M. R. Fellows, and T. J. Warnow. Two strikes against perfect phylogeny. In Lecture Notes in Computer Science 623: Proceedings of the 19th International Colloquium on Automata, Languages, and Programming, pages 273–283. Springer-Verlag, New York, NY, 1992.

    Google Scholar 

  4. R. Cole and R. Hariharan. An O(n log n) algorithm for the maximum agreement subtree problem for binary trees. In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 323–332, 1996.

    Google Scholar 

  5. M. Farach, S. Kannan, and T. Warnow. A robust model for finding optimal evolutionary trees. Algorithmica, 13(1/2):155–179, 1995.

    Google Scholar 

  6. M. Farach, T. M. Przytycka, and M. Thorup. Computing the agreement of trees with bounded degrees. In Lecture Notes in Computer Science 979: Proceedings of the Third Annual European Symposium on Algorithms, pages 381–393, 1995.

    Google Scholar 

  7. M. Farach and M. Thorup. Fast comparison of evolutionary trees (extended abstract). In Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 481–488, 1994.

    Google Scholar 

  8. M. Farach and M. Thorup. Optimal evolutionary tree comparison by sparse dynamic programming (extended abstract). In Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, pages 770–779, 1994.

    Google Scholar 

  9. C. R. Finden and A. D. Gordon. Obtaining common pruned trees. Journal of Classification, 2:255–276, 1985.

    Google Scholar 

  10. D. Gusfield. Efficient algorithms for inferring evolutionary trees. Networks, 21:19–28, 1991.

    Google Scholar 

  11. D. S. Hirschberg. Algorithms for the longest common subsequence problem. Journal of the ACM, 24(4):664–675, 1977.

    Google Scholar 

  12. J. W. Hunt and T. G. Szymanski. A fast algorithm for computing longest common subsequences. Communications of the ACM, 20:350–353, 1977.

    Google Scholar 

  13. T. Jiang, E. L. Lawler, and L. Wang. Aligning sequences via an evolutionary tree: complexity and approximation. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing, pages 760–769, 1994.

    Google Scholar 

  14. S. Kannan, E. Lawler, and T. Warnow. Determining the evolutionary tree. In Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 475–484, 1990. To appear in Journal of Algorithms.

    Google Scholar 

  15. S. K. Kannan and T. J. Warnow. Inferring evolutionary history from DNA sequences. SIAM Journal on Computing, 23(4):713–737, August 1994.

    Google Scholar 

  16. M. Y. Kao. Tree contractions and evolutionary trees. Submitted to SIAM Journal on Computing, 1996.

    Google Scholar 

  17. S. R. Kosaraju and A. L. Delcher. Optimal parallel evaluation of tree-structured computations by raking. In Lecture Notes in Computer Science 319: Proceedings of the 3rd Aegean Workshop on Computing, pages 101–110, 1988.

    Google Scholar 

  18. E. Kubicka, G. Kubicki, and F.R. McMorris. An algorithm to find agreement subtrees. Journal of Classification, 12(1):91–99, 1995.

    Google Scholar 

  19. G. L. Miller and J. H. Reif. Parallel tree contraction, part 1: Fundamentals. In Advances in Computing Research: Randomness and Computation, volume 5, pages 47–72. JAI Press, Greenwich, CT, 1989.

    Google Scholar 

  20. M. Steel and T. Warnow. Kaikoura tree theorems: Computing the maximum agreement subtree. Information Processing Letters, 48:77–82, 1993.

    Google Scholar 

  21. C. K. Wong and A. K. Chandra. Bounds for the string editing problem. Journal of the ACM, 23(1):13–16, January 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Duke University, 27708, Durham, NC, USA

    Ming-Yang Kao

Authors
  1. Ming-Yang Kao
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Giancarlo Bongiovanni Daniel Pierre Bovet Giuseppe Di Battista

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kao, MY. (1997). Tree contractions and evolutionary trees. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_81

Download citation

  • DOI: https://doi.org/10.1007/3-540-62592-5_81

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62592-6

  • Online ISBN: 978-3-540-68323-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation