Abstract
Sorting by Transpositions is an NP-hard problem. Elias and Hartman proposed a 1.375-approximation algorithm, the best ratio so far, which runs in O(n 2) time. Firoz et al. proposed an improvement to the running time, from O(n 2) down to O(n logn), using Feng and Zhu’s permutation trees. We provide counter-examples to the correctness of Firoz et al.’s strategy, showing that it is not possible to reach a component by sufficient extensions using the method proposed by them.
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References
Bafna, V., Pevzner, P.A.: Sorting by transpositions. SIAM J. Disc. Math. 11, 224–240 (1998)
Bulteau, L., Fertin, G., Rusu, I.: Sorting by transpositions is difficult. SIAM J. Discrete Math. 26(3), 1148–1180 (2012)
Cunha, L.F.I.: Limites para Distância e Diâmetro em Rearranjo de Genomas por Transposições. Master dissertation, Programa de Engenharia de Sistemas e Computação – COPPE/UFRJ, Brazil (2013)
Cunha, L.F.I., Kowada, L.A.B., de A. Hausen, R., de Figueiredo, C.M.H.: Transposition diameter and lonely permutations. In: de Souto, M.C.P., Kann, M.G. (eds.) BSB 2012. LNCS (LNBI), vol. 7409, pp. 1–12. Springer, Heidelberg (2012)
Dias, U., Dias, Z.: An improved 1.375-approximation algorithm for the transposition distance problem. In: Proceeding of the 1st ACM International Conference on Bioinformatics and Computational Biology (ACM-BCB 2010), pp. 334–337. ACM, Niagara Falls (2010)
Elias, I., Hartman, T.: A 1.375-approximation algorithm for sorting by transpositions. IEEE/ACM Trans. Comput. Biol. Bioinformatics 3(4), 369–379 (2006)
Feng, J., Zhu, D.: Faster algorithms for sorting by transpositions and sorting by block interchanges. ACM Trans. Algorithms 3(3) (2007) 1549–6325
Firoz, J.S., Hasan, M., Khan, A.Z., Rahman, M.S.: The 1.375 approximation algorithm for sorting by transpositions can run in O(n logn) time. J. Comput. Biol. 18(8), 1007–1011 (2011)
Hannehalli, S., Pevzner, P.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. J. ACM 46, 1–27 (1999)
Hartman, T., Shamir, R.: A simpler and faster 1.5-approximation algorithm for sorting by transpositions. Inf. Comput. 204(2), 275–290 (2006)
Hausen, R.A., Faria, L., Figueiredo, C.M.H., Kowada, L.A.B.: Unitary toric classes, the reality and desire diagram, and sorting by transpositions. SIAM J. Disc. Math. 24(3), 792–807 (2010)
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)
Kowada, L.A.B., de A. Hausen, R., de Figueiredo, C.M.H.: Bounds on the transposition distance for lonely permutations. In: Ferreira, C.E., Miyano, S., Stadler, P.F. (eds.) BSB 2010. LNCS (LNBI), vol. 6268, pp. 35–46. Springer, Heidelberg (2010)
Lopes, M.P., Braga, M.D.V., de Figueiredo, C.M.H., de A. Hausen, R., Kowada, L.A.B.: Analysis and implementation of sorting by transpositions using permutation trees. In: Norberto de Souza, O., Telles, G.P., Palakal, M. (eds.) BSB 2011. LNCS (LNBI), vol. 6832, pp. 42–49. Springer, Heidelberg (2011)
Sankoff, D., Leduc, G., Antoine, N., Paquin, B., Lang, B.F., Cedergren, R.: Gene sort comparisons for phylogenetic inference: evolution of the mitochondrial genome. Proc. Natl. Acad. Sci. 89(14), 6575–6579 (1992)
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Cunha, L.F.I., Kowada, L.A.B., de A. Hausen, R., de Figueiredo, C.M.H. (2013). On the 1.375-Approximation Algorithm for Sorting by Transpositions in O(n logn) Time. In: Setubal, J.C., Almeida, N.F. (eds) Advances in Bioinformatics and Computational Biology. BSB 2013. Lecture Notes in Computer Science(), vol 8213. Springer, Cham. https://doi.org/10.1007/978-3-319-02624-4_12
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DOI: https://doi.org/10.1007/978-3-319-02624-4_12
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