On the Repeat-Annotated Phylogenetic Tree Reconstruction Problem

  • Firas Swidan
  • Michal Ziv-Ukelson
  • Ron Y. Pinter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4009)


A new problem in phylogenetic inference is presented, based on recent biological findings indicating a strong association between reversals (aka inversions) and repeats. These biological findings are formalized here in a new mathematical model, called repeat-annotated phylogenetic trees (RAPT). We show that, under RAPT, the evolutionary process — including both the tree-topology as well as internal node genome orders — is uniquely determined, a property that is of major significance both in theory and in practice. Furthermore, the repeats are employed to provide linear-time algorithms for reconstructing both the genomic orders and the phylogeny, which are NP-hard problems under the classical model of sorting by reversals (SBR).


Edge Label Xanthomonas Campestris Repeat Pair Repeat Subsequence Legal Reversal 
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.
    Swidan, F., Rocha, E.P.C., Shmoish, M., Pinter, R.: An integrative method for accurate comparative genome mapping (submitted, 2005)Google Scholar
  2. 2.
    Qian, W., Jia, Y., Ren, S.X., He, Y.Q., Feng, J.X., Lu, L.F., Sun, Q., Ying, G., et al.: Comparative and functional genomic analyses of the pathogenicity of phytopathogen Xanthomonas campestris pv. campestris. Genome Res. 15(6), 757–767 (2005)CrossRefGoogle Scholar
  3. 3.
    Achaz, G., Boyer, F., Rocha, E.P.C., Viari, A., Coissac, E.: Extracting approximate repeats from large DNA sequences (2004)Google Scholar
  4. 4.
    Kowalczykowski, S.C., Dixon, D.A., Eggleston, A.K., Lauder, S.D., Rehrauer, W.M.: Biochemistry of homologous recombination in Escherichia coli. Microbiol. Rev. 58, 401–465 (1994)Google Scholar
  5. 5.
    Kececioglu, J., Sankoff, D.: Exact and approximation algorithms for the inversion distance between two permutations. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds.) CPM 1993. LNCS, vol. 684, pp. 87–105. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  6. 6.
    Kaplan, H., Shamir, R., Tarjan, R.E.: Faster and simpler algorithm for sorting signed permutations by reversals. In: Proc. 8th Ann. Symp. on Discrete Algorithms, pp. 344–351 (1997)Google Scholar
  7. 7.
    Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: Polynomial algorithm for sorting signed permutations by reversals. J. ACM 46, 1–27 (1999)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Bergeron, A., Mixtacki, J., Stoye, J.: Reversal distance without hurdles and fortresses. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 388–399. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Tannier, E., Sagot, M.F.: Sorting by reversals in subquadratic time. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 1–13. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Bender, M., Ge, D., He, S., Hu, H., Pinter, R., Skiena, S., Swidan, F.: Improved bounds on sorting with length-weighted reversals. In: Proc. 15th ACM-SIAM Symposium on Discrete Algorithms, pp. 912–921 (2004)Google Scholar
  11. 11.
    Swidan, F., Bender, M.A., Ge, D., He, S., Hu, H., Pinter, R.Y.: Sorting by length-weighted reversals: Dealing with signs and circularity. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 32–46. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Bergeron, A.: A very elementary presentation of the hannenhalli-pevzner theory. Discrete Applied Mathematics 146(2), 134–145 (2005)CrossRefMathSciNetMATHGoogle Scholar
  13. 13.
    Caprara, A.: Formulations and hardness of multiple sorting by reversals. In: Proc 3th Ann. Int. Conf. on Computational Molecular Biology, pp. 84–93. ACM Press, New York (1999)Google Scholar
  14. 14.
    Moret, B., Wang, L., Warnow, T., Wyman, S.: New approaches for reconstructing phylogenies from gene order data. In: Proc. 9th Int. Conf. Intell. Syst. Mol. Biol., pp. 165–173 (2001)Google Scholar
  15. 15.
    Bourque, G., Pevzner, P.A.: Genome-scale evolution: Reconstructing gene orders in the ancestral species. Genome Res. 12(1), 26–36 (2002)Google Scholar
  16. 16.
    Gonnet, G.H.: Handbook of Algorithms and Data Structures. International Computer Science Services (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Firas Swidan
    • 1
    • 2
  • Michal Ziv-Ukelson
    • 1
    • 3
  • Ron Y. Pinter
    • 1
  1. 1.Department of Computer ScienceTechnion – Israel Institute of TechnologyHaifaIsrael
  2. 2.Janelia Farm, Howard Hughes Medical InstituteUSA
  3. 3.School of Computer ScienceTel-Aviv UniversityTel-AvivIsrael

Personalised recommendations