A 2.25-Approximation Algorithm for Cut-and-Paste Sorting of Unsigned Circular Permutations

  • Xiaowen Lou
  • Daming Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


We consider sorting unsigned circular permutations by cut-and-paste operations. For a circular permutation, a cut-and-paste operation can be a reversal, a transposition, or a transreversal. For the sorting of signed permutations, there are several approximation algorithms allowing various combinations of these operations. For the sorting of unsigned permutations, we only know a 3-approximation algorithm and an improved algorithm with ratio 2.8386+δ, both allowing reversals and transpositions. In this paper, by new observations on the breakpoint graph, we present a 2.25-approximation algorithm for cut-and-paste sorting of unsigned circular permutations.


Performance Ratio Circular Permutation Consecutive Element Signed Permutation Black Edge 
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  1. 1.
    Bafna, V., Pevzner, P.A.: Sorting by Transpositions. SIAM J. Discrete Math. 11, 272–289 (1998)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Berman, P., Hannenhalli, S., Karpinki, 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.
    Caprara, A.: Sorting by Reversals is Difficult. In: Proc. of 1th Annual International Conference on Research in Computational Molecular Biology (RECOMB 1997), pp. 75–83 (1997)Google Scholar
  4. 4.
    Cranston, D.W., Sudborough, I.H., West, D.B.: Short Proofs for Cut-and-Paste Sorting of Permutations. Discrete Mathematics 307, 2866–2870 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gu, Q.P., Peng, S.P., Sudborough, H.: A 2-Approximation Algorithm for Genome Rearrangements by Reversals and Transpositions. Theoretical Computer Science 210, 327–339 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hartman, T., Shamir, R.: A Simpler 1.5-Approximation Algorithm for Sorting by Transpositions. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 156–169. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Hartman, T., Sharan, R.: A 1.5-Approximation Algorithm for Sorting by Transpositions and Transreversals. J. Computer and System Sciences 70, 300–320 (2005)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Hannenhalli, S., Pevzner, P.A.: Transforming Cabbage into Turnip (Polynomial Algorithm for Sorting Signed Permutations by Reversals). In: Proc. of 27th Annual ACM Symposium on Theory of Computing (STOC 1995), pp. 178–189 (1995)Google Scholar
  9. 9.
    Rahman, A., Shatabda, S., Hasan, M.: An Approximation Algorithm for Sorting by Reversals and Transpositions. J. Discrete Algorithms (in press) doi:10.1016/j.jda.2007.09.002 Google Scholar
  10. 10.
    Tannier, E., Sagot, M.-F.: Sorting by Reversals in Subquadratic Time. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 1–13. Springer, Heidelberg (2004)Google Scholar
  11. 11.
    Walter, M.E.M.T., Dias, Z., Meidanis, J.: Reversal and Transposition Distance of Linear Chromosomes. In: Proc. of String Processing and Information Retrieval (SPIRE 1998), pp. 96–102 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Xiaowen Lou
    • 1
  • Daming Zhu
    • 1
  1. 1.School of Computer Science and TechnologyShandong UniversityJinanP.R. China

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