Advertisement

Hurdles Hardly Have to Be Heeded

  • Krister M. Swenson
  • Yu Lin
  • Vaibhav Rajan
  • Bernard M. E. Moret
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5267)

Abstract

As data about genomic architecture accumulates, genomic rearrangements have attracted increasing attention. One of the main rearrangement mechanisms, inversions (also called reversals), was characterized by Hannenhalli and Pevzner and this characterization in turn extended by various authors. The characterization relies on the concepts of breakpoints, cycles, and obstructions colorfully named hurdles and fortresses. In this paper, we study the probability of generating a hurdle in the process of sorting a permutation if one does not take special precautions to avoid them (as in a randomized algorithm, for instance). To do this we revisit and extend the work of Caprara and of Bergeron by providing simple and exact characterizations of the probability of encountering a hurdle in a random permutation. Using similar methods we, for the first time, find an asymptotically tight analysis of the probability that a fortress exists in a random permutation.

Keywords

Random Permutation Genomic Architecture Frame Element Circular Permutation Common Interval 
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.
    Bader, D.A., Moret, B.M.E., Yan, M.: A linear-time algorithm for computing inversion distance between signed permutations with an experimental study. J. Comput. Biol. 8(5), 483–491 (2001); A preliminary version appeared in WADS 2001, pp. 365–376CrossRefGoogle Scholar
  2. 2.
    Bergeron, A.: A very elementary presentation of the Hannenhalli–Pevzner theory. Discrete Applied Mathematics 146(2), 134–145 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bergeron, A., Chauve, C., Hartman, T., Saint-Onge, K.: On the properties of sequences of reversals that sort a signed permutation. In: JOBIM, 99–108 (June 2002)Google Scholar
  4. 4.
    Bergeron, A., Stoye, J.: On the similarity of sets of permutations and its applications to genome comparison. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 68–79. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Caprara, A.: On the tightness of the alternating-cycle lower bound for sorting by reversals. J. Combin. Optimization 3, 149–182 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip (polynomial algorithm for sorting signed permutations by reversals). In: Proc. 27th Ann. ACM Symp. Theory of Comput. (STOC 1995), pp. 178–189. ACM Press, New York (1995)CrossRefGoogle Scholar
  7. 7.
    Hannenhalli, S., Pevzner, P.A.: Transforming mice into men (polynomial algorithm for genomic distance problems). In: Proc. 36th Ann. IEEE Symp. Foundations of Comput. Sci. (FOCS 1995), pp. 581–592. IEEE Computer Society Press, Piscataway (1995)CrossRefGoogle Scholar
  8. 8.
    Kaplan, H., Verbin, E.: Efficient data structures and a new randomized approach for sorting signed permutations by reversals. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 170–185. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Sankoff, D., Haque, L.: The distribution of genomic distance between random genomes. J. Comput. Biol. 13(5), 1005–1012 (2006)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Sturtevant, A.H., Beadle, G.W.: The relation of inversions in the x-chromosome of drosophila melanogaster to crossing over and disjunction. Genetics 21, 554–604 (1936)Google Scholar
  11. 11.
    Sturtevant, A.H., Dobzhansky, Th.: Inversions in the third chromosome of wild races of drosophila pseudoobscura and their use in the study of the history of the species. Proc. Nat’l Acad. Sci., USA 22, 448–450 (1936)CrossRefGoogle Scholar
  12. 12.
    Tannier, E., Sagot, M.: 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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Krister M. Swenson
    • 1
  • Yu Lin
    • 1
  • Vaibhav Rajan
    • 1
  • Bernard M. E. Moret
    • 1
  1. 1.Laboratory for Computational Biology and Bioinformatics, EPFL (Ecole Polytechnique Fédérale de Lausanne), and Swiss Institute of BioinformaticsLausanneSwitzerland

Personalised recommendations