Reversal Distances for Strings with Few Blocks or Small Alphabets

  • Laurent Bulteau
  • Guillaume Fertin
  • Christian Komusiewicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8486)

Abstract

We study the String Reversal Distance problem, an extension of the well-known Sorting by Reversals problem. String Reversal Distance takes two strings S and T as input, and asks for a minimum number of reversals to obtain T from S. We consider four variants: String Reversal Distance, String Prefix Reversal Distance (in which any reversal must include the first letter of the string), and the signed variants of these problems, namely Signed String Reversal Distance and Signed String Prefix Reversal Distance. We study algorithmic properties of these four problems, in connection with two parameters of the input strings: the number of blocks they contain (a block being maximal substring such that all letters in the substring are equal), and the alphabet size Σ. For instance, we show that Signed String Reversal Distance and Signed String Prefix Reversal Distance are NP-hard even if the input strings have only one letter.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bafna, V., Pevzner, P.A.: Genome rearrangements and sorting by reversals. SIAM J. Comput. 25(2), 272–289 (1996)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Caprara, A.: Sorting by reversals is difficult. In: Proc. 1st RECOMB, pp. 75–83 (1997)Google Scholar
  5. 5.
    Chen, X., Zheng, J., Fu, Z., Nan, P., Zhong, Y., Lonardi, S., Jiang, T.: Assignment of orthologous genes via genome rearrangement. IEEE ACM T. Comput. Bi. 2(4), 302–315 (2005)Google Scholar
  6. 6.
    Christie, D.A.: Genome Rearrangement Problems. PhD thesis, University of Glasgow (1998)Google Scholar
  7. 7.
    Christie, D.A., Irving, R.W.: Sorting strings by reversals and by transpositions. SIAM J. Discrete Math. 14(2), 193–206 (2001)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Fertin, G., Labarre, A., Rusu, I., Tannier, E., Vialette, S.: Combinatorics of Genome Rearrangements. Computational Molecular Biology. MIT Press (2009)Google Scholar
  9. 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)CrossRefGoogle Scholar
  10. 10.
    Fu, Z., Chen, X., Vacic, V., Nan, P., Zhong, Y., Jiang, T.: MSOAR: A high-throughput ortholog assignment system based on genome rearrangement. J. Comput. Biol. 14(9), 1160–1175 (2007)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Hurkens, C.A.J., van Iersel, L., Keijsper, J., Kelk, S., Stougie, L., Tromp, J.: Prefix reversals on binary and ternary strings. SIAM J. Discrete Math. 21(3), 592–611 (2007)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Jiang, T.: Some algorithmic challenges in genome-wide ortholog assignment. J. Comput. Sci. Technol. 25(1), 42–52 (2010)CrossRefGoogle Scholar
  13. 13.
    Radcliffe, A., Scott, A., Wilmer, E.: Reversals and transpositions over finite alphabets. SIAM J. Discrete Math. 19(1), 224 (2006)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Watterson, G., Ewens, W., Hall, T., Morgan, A.: The chromosome inversion problem. J. Theor. Biol. 99(1), 1–7 (1982)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Laurent Bulteau
    • 1
  • Guillaume Fertin
    • 2
  • Christian Komusiewicz
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  2. 2.Université de Nantes, LINA - UMR CNRS 6241France

Personalised recommendations