Advertisement

Incomplete Directed Perfect Phylogeny

  • Itsik Pe’er
  • Ron Shamir
  • Roded Sharan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1848)

Abstract

Perfect phylogeny is one of the fundamental models for studying evolution. We investigate the following generalization of the problem: The input is a species-characters matrix. The characters are binary and directed, i.e., a species can only gain characters. The difference from standard perfect phylogeny is that for some species the state of some characters is unknown. The question is whether one can complete the missing states in a way admitting a perfect phylogeny. The problem arises in classical phylogenetic studies, when some states are missing or undetermined. Quite recently, studies that infer phylogenies using inserted repeat elements in DNA gave rise to the same problem. The best known algorithm for the problem requires O(n 2 m) time for m characters and n species. We provide a near optimal ÕO(nm)-time algorithm for the problem.

Keywords

Binary Matrix Edge Deletion Dynamic Data Structure Perfect Phylogeny Canonical Matrix 
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.
    R. Agarwala and D. Fernández-Baca. A polynomial-time algorithm for the perfect phylogeny problem when the number of character states is fixed. SIAM Journal on Computing, 23(6):1216–1224, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. V. Aho, Y. Sagiv, T. G. Szymanski, and J. D. Ullman. Inferring a tree from lowest common ancestors with an application to the optimization of relational expressions. SIAM Journal on Computing, 10(3):405–421, 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    C. Benham, S. Kannan, M. Paterson, and T.J. Warnow. Hen’s teeth and whale’s feet: generalized characters and their compatibility. Journal of Computational Biology, 2(4):515–525, 1995.CrossRefGoogle Scholar
  4. 4.
    H. L. Bodlaender, M. R. Fellows, and T. J. Warnow. Two strikes against perfect phylogeny. In W. Kuich, editor, Proc. 19th IC ALP, pages 273–283, Berlin, 1992. Springer. Lecture Notes in Computer Science, Vol. 623.Google Scholar
  5. 5.
    J. H. Camin and R. R. Sokal. A method for deducing branching sequences in phylogeny. Evolution, 19:409–414, 1965.CrossRefGoogle Scholar
  6. 6.
    L. Dollo. Le lois de I’évolution. Bulletin de la Societé Belge de Géologie de Paléontologie et d’Hydrologie, 7:164–167, 1893.Google Scholar
  7. 7.
    J. Felsenstein. Inferring Phylogenies. Sinaur Associates, Sunderland, Massachusetts, 2000. In press.Google Scholar
  8. 8.
    L. R. Foulds and R. L. Graham. The Steiner problem in phylogeny is NP-complete. Advances in Applied Mathematics, 3:43–49, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    M. C. Golumbic. Matrix sandwich problems. Linear algebra and its applications, 277:239–251, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    M. C. Golumbic, H. Kaplan, and R. Shamir. Graph sandwich problems. Journal of Algorithms, 19:449–473, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    D. Gusfield. Efficient algorithms for inferring evolutionary trees. Networks, 21:19–28, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    D. Gusfield. Algorithms on Strings, Trees, and Sequences. Cambridge University Press, 1997.Google Scholar
  13. 13.
    M. Henzinger, V. King, and T.J. Warnow. Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. Algorithmica, 24:1–13, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    J. Holm, K. de Lichtenberg, and M. Thorup. Polylogarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge and biconnectivity. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC-98), pages 79–89, New York, May 23–26 1998. ACM Press.Google Scholar
  15. 15.
    S. Kannan and T. Warnow. A fast algorithm for the computation and enumeration of perfect phylogenies. SIAM Journal on Computing, 26(6):1749–1763, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    B. Klinz, R. Rudolf, and G. J. Woeginger. Permuting matrices to avoid forbidden submatrices. Discrete applied mathematics, 60:223–248, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    C. A. Meecham and G. F. Estabrook. Compatibility methods in systematics. Annual Review of Ecology and Systematics, 16:431–446, 1985.CrossRefGoogle Scholar
  18. 18.
    M. Nikaido, A. P. Rooney, and N. Okada. Phylogenetic relationships among cetartiodactyls based on insertions of short and long interspersed elements: Hippopotamuses are the closest extant relatives of whales. Proceedings of the National Academy of Science USA, 96:10261–10266, 1999.CrossRefGoogle Scholar
  19. 19.
    W. J. Le Quesne. The uniquely evolved character concept and its cladistic application. Systematic Zoology, 23:513–517, 1974.CrossRefGoogle Scholar
  20. 20.
    M. A. Steel. The complexity of reconstructing trees from qualitative characters and subtrees. Journal of Classification, 9:91–116, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    D. L. Swofford. PAUP, Phylogenetic Analysis Using Parsimony (and Other Methods). Sinaur Associates, Sunderland, Massachusetts, 1998. Version 4.Google Scholar
  22. 22.
    M. Thorup. Decremental dynamic connectivity. Journal of Algorithms, 33:229–243, 1999.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Itsik Pe’er
    • 1
  • Ron Shamir
    • 1
  • Roded Sharan
    • 1
  1. 1.Department of Computer ScienceTel-Aviv UniversityTel-AvivIsrael

Personalised recommendations