Fixed topology alignment with recombination

  • Bin Mal
  • Lusheng Wange
  • Ming Lia
Session IV
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1448)


In this paper, we study a new version of multiple sequence alignment, fixed topology alignment with recombination. We show that it can not be approximated within any constant ratio unless P = NP. For a more restricted version, we show that the problem is MAX-SNP-hard. This implies that there is no PTAS for this version unless P = NP. We also propose approximation algorithms for a special case, where each internal node has at most one recombination child and any two merge paths for different recombination nodes do not share any common node.


Binary Tree Internal Node Edit Distance Small Cost Polynomial Time Approximation Scheme 
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.
    S. Altschul and D. Lipman, Trees, stars, and multiple sequence alignment, SIAM Journal on Applied Math., 49 (1989), pp. 197–209.Google Scholar
  2. 2.
    B. DasGupta, X. He, T. Jiang, M. Li, J. Tromp and L. Zhang, On distances between phylogenetic trees, Proc. 8th Annual ACM-SIAM Symposium on Discrete Algorithms, Jan. 1997, New Orleans.Google Scholar
  3. 3.
    B. DasGupta, X. He, T. Jiang, M. Li, and J. Tromp, On the linear-cost subtree-transfer distance, submitted to Algorithmica, 1997.Google Scholar
  4. 4.
    Z. Galil and R. Ciancarlo, 11Speeding up dynamic programming with applications to molecular biology”, Theoretical Computer Science 64, pp. 107–118, 1989.Google Scholar
  5. 5.
    D. Gusfield, Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology, Cambridge University Press, 1997.Google Scholar
  6. 6.
    J. Hein, A new method that simultaneously aligns and reconstructs ancestral sequences for any number of homologous sequences, when the phylogeny is given, Mol. Biol. Evol. 6 (1989), 649–668.Google Scholar
  7. 7.
    J. Hein, Reconstructing evolution of sequences subject to recombination using parsimony, Math. Biosci. 98 (1990), 185–200.Google Scholar
  8. 8.
    J. Hein, A heuristic method to reconstruct the history of sequences subject to recombination, J. Mod. Evo. 36 (1993) 396–405.Google Scholar
  9. 9.
    J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics, 71 (1996), 153–169.Google Scholar
  10. 10.
    D. Hochbaum, Approximation Algorithms for NP-hard Problems, PWS, to appear.Google Scholar
  11. 11.
    S. K. Kannan and E. W. Myers, “An algorithm for locating non-overlapping regions of maximum alignment score”, CPM93, pp. 74–86, 1993.Google Scholar
  12. 12.
    J. Kececioglu and D. Gusfield, “ Reconstructing a history of recombinations from a set of sequences”, 5th Annual ACM-SIAM Symposium on Discrete Algorithms, Arlington, Virginia, pp. 471–480, January 1994Google Scholar
  13. 13.
    G. M. Landau and J. P. Schmidt, “An algorithm for approximate tandem repeats, CPM'93, pp. 120–133, 1993.Google Scholar
  14. 14.
    D. Sankoff, Minimal mutation trees of sequences, SIAM J. Applied Math. 28 (1975), 35–42.Google Scholar
  15. 15.
    D. Sankoff, R. J. Cedergren and G. Lapalme, Frequency of insertion-deletion, transversion, and transition in the evolution of 5S ribosomal RNA, J. Mol. Evol. 7 (1976), 133–149.Google Scholar
  16. 16.
    D. Sankoff and R. Cedergren, Simultaneous comparisons of three or more sequences related by a tree, In D. Sankoff and J. Kruskal, editors, Time warps, string edits, and macromolecules: the theory and practice of sequence comparison, pp. 253–264, Addison Wesley, 1983.Google Scholar
  17. 17.
    F. W. Stahl, “Genetic recombination”, Scientific American, 90–101, February 1987.Google Scholar
  18. 18.
    D. Swofford and G. Olson, Phylogenetic reconstruction, in Molecular Systemtics, D. Hillis and C. Moritz (eds), Sinauer Associates, Sunderland, MA, 1990.Google Scholar
  19. 19.
    J. D. Watson, N. H. Hopkins, J. W. Roberts, J. A. Steitz, A. M. Weiner, “Molecular Biology of the gene, 4th edition, Benjamin-Cummings, Menlo Park, California, 1987.Google Scholar
  20. 20.
    L. Wang and T. Jiang, On the complexity of multiple sequence alignment, Journal of Computational Biology, 1 (1994), 337–348.Google Scholar
  21. 21.
    L. Wang, T. Jiang and E.L. Lawler, Approximation algorithms for tree alignment with a given phylogeny, Algorithmica, 16 (1996), 302–315.Google Scholar
  22. 22.
    L. Wang and D. Gusfield, Improved approximation algorithms for tree alignment, Journal of Algorithms, vol. 25, pp. 255–173, 1997.Google Scholar
  23. 23.
    L. Wang, T. Jiang, and Dan Gusfield, A more efficient approximation scheme for tree alignment, Proceedings of the First Annual International Conference on Computational Molecular Biology, pp. 310–319, 1997.Google Scholar
  24. 24.
    M.S. Waterman, Introduction to Computational Biology: Maps, sequences, and genomes, Chapman and Hall, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bin Mal
    • 1
  • Lusheng Wange
    • 2
  • Ming Lia
    • 3
  1. 1.Department of MathematicsPeking UniversityBeijingP.R. China
  2. 2.Department of Computer ScienceCity University of Hong KongKowloonHong Kong
  3. 3.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations