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On the Diameter of Rearrangement Problems

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Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 8542))

Abstract

When we consider the Genome Rearrangements area, the problems of finding the distance of a permutation and finding the diameter of all permutations of the same size are the most common studied. In this paper, we considered problems for which no known results were presented regarding their diameters. We present some families of permutations whose distance is identical to the diameter for small sizes. They allowed us to gave bounds for the diameters of the problems we considered, as well as conjectures regarding the exact value.

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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. 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 

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

    MATH  MathSciNet  Google Scholar 

  4. 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 

  5. Chitturi, B., Fahle, W., Meng, Z., Morales, L., Shields, C.O., Sudborough, I.H., Voit, W.: An (18/11)n Upper Bound for Sorting by Prefix Reversals. Theoretical Computer Science 410(36), 3372–3390 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chitturi, B., Sudborough, I.H.: Bounding Prefix Transposition Distance for Strings and Permutations. Theoretical Computer Science 421, 15–24 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cibulka, J.: On Average and Highest Number of Flips in Pancake Sorting. Theoretical Computer Science 412(8-10), 822–834 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. 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 

  9. Elias, I., Hartman, T.: A 1.375-Approximation Algorithm for Sorting by Transpositions. 375-Approximation Algorithm for Sorting by Transpositions 3(4), 369–379 (2006)

    Google Scholar 

  10. Eriksson, H., Eriksson, K., Karlander, J., Svensson, L., Wastlund, J.: Sorting a Bridge Hand. Discrete Mathematics 241(1-3), 289–300 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Fertin, G., Labarre, A., Rusu, I., Tannier, É., Vialette, S.: Combinatorics of Genome Rearrangements. In: Computational Molecular Biology. MIT Press (2009)

    Google Scholar 

  12. Galvão, G.R., Dias, Z.: Computing Rearrangement Distance of Every Permutation in the Symmetric Group. In: Chu, W.C., Wong, W.E., Palakal, M.J., Hung, C.C. (eds.) Proceedings of the 26th ACM Symposium on Applied Computing (SAC 22011), pp. 106–107. ACM (2011)

    Google Scholar 

  13. Gates, W.H., Papadimitriou, C.H.: Bounds for Sorting by Prefix Reversal. Discrete Mathematics 27(1), 47–57 (1979)

    Article  MathSciNet  Google Scholar 

  14. 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)

    Article  MATH  MathSciNet  Google Scholar 

  15. Heydari, M.H., Sudborough, I.H.: On the Diameter of the Pancake Network. Journal of Algorithms 25(1), 67–94 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Labarre, A.: Edit Distances and Factorisations of Even Permutations. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 635–646. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  17. Lintzmayer, C.N., Dias, Z.: On Sorting of Signed Permutations by Prefix and Suffix Reversals and Transpositions. In: Dediu, A.H., Martín-Vide, C., Truthe, B. (eds.) Proceedings of the 1st International Conference on Algorithms for Computational Biology (AlCoB 2014), Tarragona, Spain, pp. 1–12. Springer (2014)

    Google Scholar 

  18. 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)

    Chapter  Google Scholar 

  19. Meidanis, J., Walter, M.M.T., Dias, Z.: A Lower Bound on the Reversal and Transposition Diameter. Journal of Computational Biology 9(5), 743–745 (2002)

    Article  Google Scholar 

  20. 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)

    Google Scholar 

  21. 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), pp. 96–102. IEEE Computer Society, Santa Cruz (1998)

    Google Scholar 

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Lintzmayer, C.N., Dias, Z. (2014). On the Diameter of Rearrangement Problems. 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_13

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  • DOI: https://doi.org/10.1007/978-3-319-07953-0_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07952-3

  • Online ISBN: 978-3-319-07953-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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