Abstract
In computational biology, genome rearrangements is a field in which we study mutational events affecting large portions of a genome. One such event is the transposition, that changes the position of contiguous blocks of genes inside a chromosome. This event generates the problem of transposition distance, that is to find the minimal number of transpositions transforming one chromosome into another. It is not known whether this problem is \(\mathcal{NP}\)-hard or has a polynomial time algorithm. Some approximation algorithms have been proposed in the literature, whose proofs are based on exhaustive analysis of graphical properties of suitable cycle graphs. In this paper, we follow a different, more formal approach to the problem, and present a 1.5-approximation algorithm using an algebraic formalism. Besides showing the feasibility of the approach, the presented algorithm exhibits good results, as our experiments show.
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References
Bader, D.A., Moret, B.M.E., Yan, M.: A linear-time algorithm for computing inversion distance between signed permutations with an experimental study. Journal of Computational Biology 8(5), 483–491 (2001)
Bafna, V., Pevzner, P.A.: Sorting by transpositions. In: Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, USA, January 1995, pp. 614–623 (1995)
Bafna, V., Pevzner, P.A.: Sorting by transpositions. SIAM Journal on Discrete Mathematics 11(2), 224–240 (1998)
Benoît-Gagné, M., Hamel, S.: A new and faster method of sorting by transpositions. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, vol. 4580, pp. 131–141. Springer, Heidelberg (2007)
Christie, D.A.: Sorting permutations by block-interchanges. Information Processing Letters 60(4), 165–169 (1996)
Christie, D.A.: Genome Rearrangement Problems. PhD thesis, Glasgow University (1998)
Elias, I., Hartman, T.: A 1.375-approximation algorithm for sorting by transpositions. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), vol. 3692, pp. 204–215. Springer, Heidelberg (2005)
Hannenhalli, S., Pevzner, P.A.: Transforming men into mice (polynomial algorithm for genomic distance problem). In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS 1995), October 1995, pp. 581–592. IEEE Computer Society Press, Los Alamitos (1995)
Hartman, T.: A simpler 1.5-approximation algorithm for sorting by transpositions. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 156–169. Springer, Heidelberg (2003)
Hartman, T., Shamir, R.: A simpler and faster 1.5-approximation algorithm for sorting by transpositions. In: Proceedings of CPM 2003, pp. 156–169 (2003) (extended version)
Honda, M.I.: Implementation of the algorithm of Hartman for the problem of sorting by transpositions. Master’s thesis, Department of Computer Science, University of Brasilia (in portuguese) (2004)
Meidanis, J., Dias, Z.: An alternative algebraic formalism for genome rearrangements. In: Sankoff, D., Nadeau, J.H. (eds.) Comparative Genomics: Empirical and Analyitical Approaches to Gene Order Dynamics, Map Alignment and Evolution of Gene Families, pp. 213–223. Kluwer Academic Publishers, Dordrecht (November 2000)
Meidanis, J., Walter, M.E.M.T., Dias, Z.: Transposition distance between a permutation and its reverse. In: Baeza-Yates, R. (ed.) Proceedings of the 4th South American Workshop on String Processing (WSP 1997), Valparaiso, Chile, pp. 70–79. Carleton University Press (1997)
Mira, C., Meidanis, J.: Algebraic formalism for genome rearrangements (part 1). Technical Report IC-05-10, Institute of Computing - University of Campinas (June 2005)
Mira, C.V.G., Meidanis, J.: Analysis of sorting by transpositions based on algebraic formalism. In: The Eighth Annual International Conference on Research in Computational Molecular Biology (RECOMB 2004) (March 2004)
Walter, M.E.M.T., Curado, L.R.A.F., Oliveira, A.G.: Working on the problem of sorting by transpositions on genome rearrangements. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 372–383. Springer, Heidelberg (2003)
Walter, M.E.M.T., Dias, Z., Meidanis, J.: A new approach for approximating the transposition distance. In: String Processing and Information Retrieval - SPIRE 2000, pp. 199–208 (2000)
Walter, M.E.M.T., Oliveira, E.T.G.: Extending the theory of Bafna and Pevzner for the problem of sorting by transpositions. Tendências em Matemática Aplicada e Computacional - TEMA - SBMAC 3(1), 213–222 (2002) (in portuguese)
Walter, M.E.M.T., Soares, L.S.N., Dias, Z.: Branch-and-bound algorithms for the problem of sorting by transpositions on genome rearrangements. In: Proceedings of the 26th Congress of the Brazilian Computer Society, XXXIII Seminário integrado de hardware e software – SEMISH, pp. 69–81 (2006)
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Mira, C.V.G., Dias, Z., Santos, H.P., Pinto, G.A., Walter, M.E.M.T. (2008). Transposition Distance Based on the Algebraic Formalism. In: Bazzan, A.L.C., Craven, M., Martins, N.F. (eds) Advances in Bioinformatics and Computational Biology. BSB 2008. Lecture Notes in Computer Science(), vol 5167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85557-6_11
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DOI: https://doi.org/10.1007/978-3-540-85557-6_11
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