Abstract
Feng and Zhu defined the permutation tree structure to achieve a running time of O(nlogn) for Hartman and Shamir’s 1.5-approximation algorithm for sorting genomes by transpositions. The present work describes the first available implementation of this algorithm using permutation trees. Our analysis of Hartman and Shamir’s algorithm also leads to a modified 1.5-approximation algorithm that achieves in most cases a shorter sequence of transpositions that sorts a given permutation. Although our modified algorithm has a worst-case running time of O(n 2logn), in our experiments using real genomic data the running time is still very small.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bafna, V., Pevzner, P.A.: Sorting by transpositions. SIAM J. Disc. Math. 11(2), 224–240 (1998)
Boore, J.L.: The duplication/random loss model for gene rearrangement exemplified by mitochondrial genomes of deuterostome animals. In: Sankoff, D., Nadeau, J.H. (eds.) Comparative Genomics, pp. 133–148. Kluwer Academic Publishers, Dordrecht (2000)
Bulteau, L., Fertin, G., Rusu, I.: Sorting by transpositions is difficult. arXiv: 1011.1157v1 [cs.DS] (November 2010)
Dias, U., Dias, Z.: An improved 1.375-approximation algorithm for the transposition distance problem. In: Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology, BCB 2010, pp. 334–337. ACM, New York (2010)
Elias, I., Hartman, T.: A 1.375-approximation algorithm for sorting by transpositions. IEEE/ACM Trans. Comput. Biol. and 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 (August 2007)
Firoz, J., Hasan, M., Khan, A., Rahman, M.: The 1.375 approximation algorithm for sorting by transpositions can run in O(n logn) time. In: Rahman, M., Fujita, S. (eds.) WALCOM 2010. LNCS, vol. 5942, pp. 161–166. Springer, Heidelberg (2010)
Hartman, T.: Combinatorial algorithms for genome rearrangements and DNA oligonucleotide arrays. Ph.D. thesis, Weizmann Institute of Science (2004)
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)
Kowada, L., de, A., Hausen, R., de Figueiredo, C.: Bounds on the transposition distance for lonely permutations. In: Ferreira, C., Miyano, S., Stadler, P. (eds.) BSB 2010. LNCS, vol. 6268, pp. 35–46. Springer, Heidelberg (2010)
Lin, G., Xue, G.: Signed genome rearrangement by reversals and transpositions: models and approximations. Theoret. Comput. Sci. 259(1-2), 513–531 (2001)
Lu, L., Yang, Y.: A lower bound on the transposition diameter. SIAM J. Disc. Math. 24(4), 1242–1249 (2010)
Sankoff, D., Leduc, G., Antoine, N., Paquin, B., Lang, B.F., Cedergren, R.: Gene order comparisons for phylogenetic inference: evolution of the mitochondrial genome. Proc. Natl. Acad. Sci. 89(14), 6575–6579 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lopes, M.P., Braga, M.D.V., de Figueiredo, C.M.H., de A. Hausen, R., Kowada, L.A.B. (2011). Analysis and Implementation of Sorting by Transpositions Using Permutation Trees. In: Norberto de Souza, O., Telles, G.P., Palakal, M. (eds) Advances in Bioinformatics and Computational Biology. BSB 2011. Lecture Notes in Computer Science(), vol 6832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22825-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-22825-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22824-7
Online ISBN: 978-3-642-22825-4
eBook Packages: Computer ScienceComputer Science (R0)