The Problem of Chromosome Reincorporation in DCJ Sorting and Halving

  • Jakub Kováč
  • Marília D. V. Braga
  • Jens Stoye
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6398)

Abstract

We study two problems in the double cut and join (DCJ) model: sorting – transforming one multilinear genome into another and halving – transforming a duplicated genome into a perfectly duplicated one. The DCJ model includes rearrangement operations such as reversals, translocations, fusions and fissions. We can also mimic transpositions or block interchanges by two operations: we extract an appropriate segment of a chromosome, creating a temporary circular chromosome, and in the next step we reinsert it in its proper place. Existing linear-time algorithms solving both problems ignore the constraint of reincorporating the temporary circular chromosomes immediately after their creation. For the restricted sorting problem only a quadratic algorithm was known, whereas the restricted halving problem was stated as open by Tannier, Zheng, and Sankoff. In this paper we address this constraint and show how to solve the problem of sorting in O(nlogn) time and halving in O(n3/2) time.

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References

  1. 1.
    Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21, 3340–3346 (2005)CrossRefPubMedGoogle Scholar
  2. 2.
    Bergeron, A., Mixtacki, J., Stoye, J.: A unifying view of genome rearrangements. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS (LNBI), vol. 4175, pp. 163–173. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Christie, D.A.: Sorting permutations by block-interchanges. Inf. Process. Lett. 60, 165–169 (1996)CrossRefGoogle Scholar
  4. 4.
    Feng, J., Zhu, D.: Faster algorithms for sorting by transpositions and sorting by block interchanges. ACM Transactions on Algorithms 3 (2007)Google Scholar
  5. 5.
    Swenson, K.M., Rajan, V., Lin, Y., Moret, B.M.E.: Sorting signed permutations by inversions in O(nlogn) time. JCB 17, 489–501 (2010)Google Scholar
  6. 6.
    Warren, R., Sankoff, D.: Genome halving with double cut and join. JBCB 7, 357–371 (2009)Google Scholar
  7. 7.
    Mixtacki, J.: Genome halving under DCJ revisited. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 276–286. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Tannier, E., Zheng, C., Sankoff, D.: Multichromosomal median and halving problems under different genomic distances. BMC Bioinformatics 10 (2009)Google Scholar
  9. 9.
    El-Mabrouk, N., Sankoff, D.: The reconstruction of doubled genomes. SIAM J. Comput. 32, 754–792 (2003)CrossRefGoogle Scholar
  10. 10.
    Kaplan, H., Verbin, E.: Sorting signed permutations by reversals, revisited. J. Comput. Syst. Sci. 70(3), 321–341 (2005)CrossRefGoogle Scholar
  11. 11.
    Han, Y.: Improving the efficiency of sorting by reversals. In: Arabnia, H.R., Valafar, H. (eds.) BIOCOMP, pp. 406–409. CSREA Press (2006)Google Scholar
  12. 12.
    Chrobak, M., Szymacha, T., Krawczyk, A.: A data structure useful for finding hamiltonian cycles. Theor. Comput. Sci. 71, 419–424 (1990)CrossRefGoogle Scholar
  13. 13.
    Tannier, E., Bergeron, A., Sagot, M.F.: Advances on sorting by reversals. Discrete Applied Mathematics 155, 881–888 (2007)CrossRefGoogle Scholar
  14. 14.
    Ozery-Flato, M., Shamir, R.: An \(O(n^{3/2}\sqrt{\log (n)})\) algorithm for sorting by reciprocal translocations. In: Lewenstein, M., Valiente, G. (eds.) CPM 2006. LNCS, vol. 4009, pp. 258–269. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Bérard, S., Chateau, A., Chauve, C., Paul, C., Tannier, E.: Computation of perfect dcj rearrangement scenarios with linear and circular chromosomes. JCB 16, 1287–1309 (2009), PMID: 19803733Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jakub Kováč
    • 1
    • 2
  • Marília D. V. Braga
    • 2
  • Jens Stoye
    • 2
  1. 1.Department of Computer ScienceComenius UniversitySlovakia
  2. 2.AG Genominformatik, Technische FakultätUniversität BielefeldGermany

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