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Sorting Permutations by Prefix and Suffix Versions of Reversals and Transpositions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

Abstract

Reversals and transpositions are the most common kinds of genome rearrangements, which allow us to establish the divergence between individuals along evolution. When the rearrangements affect segments from the beginning or from the end of the genome, we say they are prefix or suffix rearrangements, respectively. This paper presents the first approximation algorithms for the problems of Sorting by Prefix Reversals and Suffix Reversals, Sorting by Prefix Transpositions and Suffix Transpositions and Sorting by Prefix Reversals, Prefix Transpositions, Suffix Reversals and Suffix Transpositions, all of them with factor 2. We also present the intermediary algorithms that lead us to the main results.

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References

  1. Bafna, V., Pevzner, P.A.: Genome Rearrangements and Sorting by Reversals. In: Proceedings of the 34th Annual Symposium on Foundations of Computer Science (FOCS 1993), pp. 148–157 (1993)

    Google Scholar 

  2. Bafna, V., Pevzner, P.A.: Sorting by Transpositions. SIAM Journal on Discrete Mathematics 11(2), 224–240 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Berman, P., Hannenhalli, S., Karpinski, M.: 1.375-Approximation Algorithm for Sorting by Reversals. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 200–210. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. Bulteau, L., Fertin, G., Rusu, I.: Pancake flipping is hard. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 247–258. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Bulteau, L., Fertin, G., Rusu, I.: Sorting by Transpositions Is Difficult. SIAM Journal on Computing 26(3), 1148–1180 (2012)

    MATH  MathSciNet  Google Scholar 

  6. Caprara, A.: Sorting Permutations by Reversals and Eulerian Cycle Decompositions. SIAM Journal on Discrete Mathematics 12(1), 91–110 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dias, Z., Meidanis, J.: Sorting by Prefix Transpositions. In: Laender, A.H.F., Oliveira, A.L. (eds.) SPIRE 2002. LNCS, vol. 2476, pp. 65–76. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Elias, I., Hartman, T.: A 1.375-Approximation Algorithm for Sorting by Transpositions. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(4), 369–379 (2006)

    Article  Google Scholar 

  9. Fischer, J., Ginzinger, S.W.: A 2-Approximation Algorithm for Sorting by Prefix Reversals. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 415–425. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Galvão, G.R., Dias, Z.: On the performance of sorting permutations by prefix operations. In: Proceedings of the 4th International Conference on Bioinformatics and Computational Biology (BICoB 2012), Las Vegas, Nevada, USA, pp. 102–107 (2012)

    Google Scholar 

  11. Sharmin, M., Yeasmin, R., Hasan, M., Rahman, A., Rahman, M.S.: Pancake Flipping with Two Spatulas. Electronic Notes in Discrete Mathematics 36, 231–238 (2010), International Symposium on Combinatorial Optimization (ISCO 2010)

    Google Scholar 

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© 2014 Springer-Verlag Berlin Heidelberg

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Lintzmayer, C.N., Dias, Z. (2014). Sorting Permutations by Prefix and Suffix Versions of Reversals and Transpositions. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_58

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  • DOI: https://doi.org/10.1007/978-3-642-54423-1_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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