Abstract
The problem of sorting a signed permutation by reversals is inspired by genome rearrangements in computational molecular biology. Given two genomes represented as two signed permutations of the same elements (e.g. orthologous genes), the problem consists in finding a most parsimonious scenario of reversals that transforms one genome into the other. We propose a method for sorting a signed permutation by reversals in time \(O(n\sqrt{n\log n})\). The best known algorithms run in time O(n 2), the main obstacle to an improvement being a costly operation of detection of so-called “safe” reversals. We bypass this detection and, using the same data structure as a previous random approximation algorithm, we achieve the same subquadratic complexity for finding an exact optimal solution. This answers an open question by Ozery-Flato and Shamir whether a subquadratic complexity could ever be achieved for solving the problem.
Work supported by the French program bioinformatique Inter-EPST 2002 “Algorithms for Modelling and Inference Problems in Molecular Biology”.
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References
Bader, D.A., Moret, B.M.E., Yan, M.: A linear-time algorithm for compting inversion distance between signed permutations with an experimental study. In: Proceedings of the 7th Workshop on Algorithms and Data Structures, pp. 365–376 (2001)
Bergeron, A., Mixtacki, J., Stoye, J.: The Reversal Distance Problem. In: Gascuel, O. (ed.) Mathematics of Evolution and Phylogeny, Oxford University Press, Oxford (to appear)
Berman, P., Hannenhalli, S.: Fast sorting by reversals. In: Hirschberg, D.S., Meyers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 168–185. Springer, Heidelberg (1996)
Hannenhalli, S., Pevzner, P.: Transforming cabbage into turnip polynomial algorithm for sorting signed permutations by reversals. In: Proceedings of the 27th ACM Symposium on Theory of Computing, pp. 178–189 (1995)
Kaplan, H., Shamir, R., Tarjan, R.E.: Faster and simpler algorithm for sorting signed permutations by reversals. SIAM Journal on Computing 29, 880–892 (1999)
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)
Ozery-Flato, M., Shamir, R.: Two notes on genome rearrangement. Journal of Bioinformatics and Computational Biology 1, 71–94 (2003)
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© 2004 Springer-Verlag Berlin Heidelberg
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Tannier, E., Sagot, MF. (2004). Sorting by Reversals in Subquadratic Time. In: Sahinalp, S.C., Muthukrishnan, S., Dogrusoz, U. (eds) Combinatorial Pattern Matching. CPM 2004. Lecture Notes in Computer Science, vol 3109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27801-6_1
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DOI: https://doi.org/10.1007/978-3-540-27801-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22341-2
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