Abstract
A reversal inverts a segment and the signs of the elements of this segment in a permutation. A transposition exchanges the position of two consecutive segments. These are the most common kinds of genome rearrangements. In this paper, we introduce the study of prefix and suffix versions of these operations, that is, when only segments of the beginning or of the end are involved, when considering signed permutations. We gave asymptotic approximation algorithms of factor two for three new problems: when prefix and suffix reversals are allowed, when prefix reversals and prefix transpositions are allowed, and when prefix and suffix reversals and prefix and suffix transpositions are allowed.
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References
Cibulka, J.: On Average and Highest Number of Flips in Pancake Sorting. Theoretical Computer Science 412(8-10), 822–834 (2011)
Cohen, D.S., Blum, M.: On the Problem of Sorting Burnt Pancakes. Discrete Applied Mathematics 61(2), 105–120 (1995)
Fertin, G., Labarre, A., Rusu, I., Tannier, É., Vialette, S.: Combinatorics of Genome Rearrangements. The MIT Press (2009)
Galvão, G.R.: Uma Ferramenta de Auditoria para Algoritmos de Rearranjo de Genomas. Master’s thesis, University of Campinas, Institute of Computing, Campinas, São Paulo, Brazil (2012) (in Portuguese)
Gates, W.H., Papadimitriou, C.H.: Bounds for Sorting by Prefix Reversal. Discrete Mathematics 27(1), 47–57 (1979)
Gu, Q.P., Peng, S., Sudborough, I.H.: A 2-Approximation Algorithm for Genome Rearrangements by Reversals and Transpositions. Theoretical Computer Science 210(2), 327–339 (1999)
Hannenhalli, S., Pevzner, P.A.: Transforming Cabbage into Turnip: Polynomial Algorithm for Sorting Signed Permutations by Reversals. Journal of the ACM 46(1), 1–27 (1999)
Hartman, T., Sharan, R.: A 1. 5-Approximation Algorithm for Sorting by Transpositions and Transreversals. Journal of Computer and System Sciences 70(3), 300–320 (2005)
Heydari, M.H., Sudborough, I.H.: On the Diameter of the Pancake Network. Journal of Algorithms 25(1), 67–94 (1997)
Lin, G.H., Xue, G.: Signed Genome Rearrangement by Reversals and Transpositions: Models and Approximations. Theoretical Computer Science 259(1-2), 513–531 (2001)
Lintzmayer, C.N., Dias, Z.: Sorting Permutations by Prefix and Suffix Versions of Reversals and Transpositions. In: Pardo, A., Viola, A. (eds.) LATIN 2014. LNCS, vol. 8392, pp. 671–682. Springer, Heidelberg (2014)
Sharmin, M., Yeasmin, R., Hasan, M., Rahman, A., Rahman, M.S.: Pancake Flipping with Two Spatulas. In: International Symposium on Combinatorial Optimization (ISCO 2010). Electronic Notes in Discrete Mathematics, vol. 36, pp. 231–238 (2010)
Tannier, E., Bergeron, A., Sagot, M.F.: Advances on Sorting by Reversals. Discrete Applied Mathematics 155(6-7), 881–888 (2007)
Walter, M.E.M.T., Dias, Z., Meidanis, J.: Reversal and Transposition Distance of Linear Chromosomes. In: Proceedings of the 5th International Symposium on String Processing and Information Retrieval (SPIRE 1998), Santa Cruz, Bolivia, pp. 96–102. IEEE Computer Society (1998)
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Lintzmayer, C.N., Dias, Z. (2014). On Sorting of Signed Permutations by Prefix and Suffix Reversals and Transpositions. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Algorithms for Computational Biology. AlCoB 2014. Lecture Notes in Computer Science(), vol 8542. Springer, Cham. https://doi.org/10.1007/978-3-319-07953-0_12
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DOI: https://doi.org/10.1007/978-3-319-07953-0_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07952-3
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