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Polynomial-Time Algorithm for Sorting by Generalized Translocations

  • Xiao Yin
  • Daming Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)

Abstract

Translocation is a prevalent rearrangement event in the evolution of multi-chromosomal species which exchanges ends between two chromosomes. A translocation is reciprocal if none of the exchanged ends is empty; otherwise, non-reciprocal. Given two signed multi-chromosomal genomes A and B, the problem of sorting by translocations is to find a shortest sequence of translocations transforming A into B. Several polynomial algorithms have been presented, all of them only allowing reciprocal translocations. Thus they can only be applied to a pair of genomes having the same set of chromosome ends. Such a restriction can be removed if non-reciprocal translocations are also allowed. In this paper, for the first time, we study the problem of sorting by generalized translocations, which allows both reciprocal translocations and non-reciprocal translocations. We present an exact formula for computing the generalized translocation distance, which leads to a polynomial algorithm for this problem.

Keywords

Algorithm genome rearrangement translocation 

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References

  1. 1.
    Bafna, V., Pevzner, P.: Sorting by reversals: Genome rearrangements in plant organelles and evolutionary history of x chromosome. Molecular Biology Evolution 12, 239–246 (1995)Google Scholar
  2. 2.
    Hannenhalli, S., Pevzner, P.: Transforming men into mice: Polynomial algorithm for genomic distance problem. In: Proc. 36th Ann. Symp. Foundations of Computer Science (FOCS 1995), pp. 581–592 (1995)Google Scholar
  3. 3.
    Hannenhalli, S., Pevzner, P.: Transforming cabbage into turnip: Polynomial algorithm for sorting signed permutations by reversals. Journal of the ACM 46, 1–27 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kececioglu, J.D., Ravi, R.: of mice and men: Algorithms for evolutionary distance between genomes with translocation. In: Proc. 6th Annu. ACM-SIAM Symp. Discrete Algorithms (SODA 1995), pp. 604–613 (1995)Google Scholar
  5. 5.
    Hannenhalli, S.: Polynomial algorithm for computing translocation distance between genomes. Discrete Applied Mathematics 71, 137–151 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bergeron, A., Mixtacki, J., Stoye, J.: On sorting by translocations. Journal of Computational Biology 13, 567–578 (2006)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Zhu, D.M., Ma, S.H.: Improved polynomial-time algorithm for computing translocation distance between genomes. The Chinese Journal of Computers 25, 189–196 (2002)MathSciNetGoogle Scholar
  8. 8.
    Wang, L.S., Zhu, D.M., Liu, X.W., Ma, S.H.: An O(n 2) algorithm for signed translocation. Journal of Computer and System Sciences 70, 284–299 (2005)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Ozery-Flato, M., Shamir, R.: An \(n^{3/2}\sqrt{log(n)}\) algorithm for sorting by reciprocal translocations. In: Proc. 17th Ann. Symp. Combinatorial Pattern Matching (CPM 2006), pp. 258–269 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Xiao Yin
    • 1
  • Daming Zhu
    • 1
  1. 1.School of Computer Science and TechnologyShandong UniversityJinanP.R. China

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