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Length and Symmetry on the Sorting by Weighted Inversions Problem

  • Christian Baudet
  • Ulisses Dias
  • Zanoni Dias
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8826)

Abstract

Large-scale mutational events that occur when stretches of DNA sequence move throughout genomes are called genome rearrangement events. In bacteria, inversions are one of the most frequently observed rearrangements. In some bacterial families, inversions are biased in favor of symmetry as shown by recent research [6, 8, 10]. In addition, several results suggest that short segment inversions are more frequent in the evolution of microbial genomes [4,6,15]. Despite the fact that symmetry and length of the reversed segments seem very important, they have not been considered together in any problem in the genome rearrangement field. Here, we define the problem of sorting genomes (or permutations) using inversions whose costs are assigned based on their lengths and asymmetries. We present five procedures and we assess these procedure performances on small sized permutations. The ideas presented in this paper provide insights to solve the problem and set the stage for a proper theoretical analysis.

Keywords

Genome Rearrangement Greedy Heuristic Identity Permutation Greedy Function Reversed Segment 
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.

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References

  1. 1.
    Arruda, T.S., Dias, U., Dias, Z.: Heuristics for the sorting by length-weighted inversion problem. In: Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics, pp. 498–507 (2013)Google Scholar
  2. 2.
    Arruda, T.S., Dias, U., Dias, Z.: Heuristics for the sorting by length-weighted inversions problem on signed permutations. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) AlCoB 2014. LNCS, vol. 8542, pp. 59–70. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  3. 3.
    Bender, M.A., Ge, D., He, S., Hu, H., Pinter, R.Y., Skiena, S., Swidan, F.: Improved bounds on sorting by length-weighted reversals. Journal of Computer and System Sciences 74(5), 744–774 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Blanchette, M., Kunisawa, T., Sankoff, D.: Parametric genome rearrangement. Gene 172(1), C11–C17 (1996)Google Scholar
  5. 5.
    Caprara, A.: Sorting permutations by reversals and Eulerian cycle decompositions. SIAM Journal on Discrete Mathematics 12(1), 91–110 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Darling, A.E., Miklós, I., Ragan, M.A.: Dynamics of genome rearrangement in bacterial populations. PLoS Genetics 4(7), e1000128 (2008)Google Scholar
  7. 7.
    Dias, U., Baudet, C., Dias, Z.: Greedy randomized search procedure to sort genomes using symmetric, almost-symmetric and unitary inversions. In: Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics, BCB 2013, pp. 181–190. ACM, New York (2013)Google Scholar
  8. 8.
    Dias, U., Dias, Z., Setubal, J.C.: A simulation tool for the study of symmetric inversions in bacterial genomes. In: Tannier, E. (ed.) RECOMB-CG 2010. LNCS, vol. 6398, pp. 240–251. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Dias, Z., Dias, U., Setubal, J.C., Heath, L.S.: Sorting genomes using almost-symmetric inversions. In: Proceedings of the 27th Symposium On Applied Computing (SAC 2012), Riva del Garda, Italy, pp. 1–7 (2012)Google Scholar
  10. 10.
    Eisen, J.A., Heidelberg, J.F., White, O., Salzberg, S.L.: Evidence for symmetric chromosomal inversions around the replication origin in bacteria. Genome Biology 1(6), research0011.1–research0011.9 (2000)Google Scholar
  11. 11.
    Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. Journal of the ACM 46(1), 1–27 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Lefebvre, J.F., El-Mabrouk, N., Tillier, E., Sankoff, D.: Detection and validation of single gene inversions. Bioinformatics 19(suppl 1), i190–196 (2003) Google Scholar
  13. 13.
    Ohlebusch, E., Abouelhoda, M.I., Hockel, K., Stallkamp, J.: The median problem for the reversal distance in circular bacterial genomes. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 116–127. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Pinter, R.Y., Skiena, S.: Genomic sorting with length-weighted reversals. Genome Informatics 13, 2002 (2002)Google Scholar
  15. 15.
    Sankoff, D.: Short inversions and conserved gene cluster. Bioinformatics 18(10), 1305–1308 (2002)CrossRefGoogle Scholar
  16. 16.
    Sankoff, D., Lefebvre, J.F., Tillier, E., Maler, A., El-Mabrouk, N.: The distribution of inversion lengths in bacteria. In: Lagergren, J. (ed.) RECOMB-WS 2004. LNCS (LNBI), vol. 3388, pp. 97–108. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Swidan, F., Bender, M., Ge, D., He, S., Hu, H., Pinter, R.: 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

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Christian Baudet
    • 1
  • Ulisses Dias
    • 2
  • Zanoni Dias
    • 2
  1. 1.INRIA Bamboo TeamUniversité Lyon IFrance
  2. 2.Institute of ComputingUniversity of CampinasBrazil

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