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(n 3/2) time.
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References
Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21, 3340–3346 (2005)
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)
Christie, D.A.: Sorting permutations by block-interchanges. Inf. Process. Lett. 60, 165–169 (1996)
Feng, J., Zhu, D.: Faster algorithms for sorting by transpositions and sorting by block interchanges. ACM Transactions on Algorithms 3 (2007)
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)
Warren, R., Sankoff, D.: Genome halving with double cut and join. JBCB 7, 357–371 (2009)
Mixtacki, J.: Genome halving under DCJ revisited. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 276–286. Springer, Heidelberg (2008)
Tannier, E., Zheng, C., Sankoff, D.: Multichromosomal median and halving problems under different genomic distances. BMC Bioinformatics 10 (2009)
El-Mabrouk, N., Sankoff, D.: The reconstruction of doubled genomes. SIAM J. Comput. 32, 754–792 (2003)
Kaplan, H., Verbin, E.: Sorting signed permutations by reversals, revisited. J. Comput. Syst. Sci. 70(3), 321–341 (2005)
Han, Y.: Improving the efficiency of sorting by reversals. In: Arabnia, H.R., Valafar, H. (eds.) BIOCOMP, pp. 406–409. CSREA Press (2006)
Chrobak, M., Szymacha, T., Krawczyk, A.: A data structure useful for finding hamiltonian cycles. Theor. Comput. Sci. 71, 419–424 (1990)
Tannier, E., Bergeron, A., Sagot, M.F.: Advances on sorting by reversals. Discrete Applied Mathematics 155, 881–888 (2007)
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)
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: 19803733
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Kováč, J., Braga, M.D.V., Stoye, J. (2010). The Problem of Chromosome Reincorporation in DCJ Sorting and Halving. In: Tannier, E. (eds) Comparative Genomics. RECOMB-CG 2010. Lecture Notes in Computer Science(), vol 6398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16181-0_2
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DOI: https://doi.org/10.1007/978-3-642-16181-0_2
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