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Minimum Common String Partition Revisited

  • Haitao Jiang
  • Binhai Zhu
  • Daming Zhu
  • Hong Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6213)

Abstract

Minimum Common String Partition (MCSP) has drawn much attention due to its application in genome rearrangement. In this paper, we investigate three variants of MCSP: MCSP c , which requires that there are at most c symbols in the alphabet; d-MCSP, which requires the occurrence of each symbol to be bounded by d; and x-balance MCSP, which requires the length of blocks not being x away from the average length. We show that MCSP c is NP-hard when c ≥ 2. As for d-MCSP, we present an FPT algorithm which runs in O *((d!) k ) time. As it is still unknown whether an FPT algorithm only parameterized on k exists for the general case of MCSP, we also devise an FPT algorithm for the special case x-balance MCSP parameterized on both k and x.

Keywords

Greedy Algorithm Approximation Ratio Genome Rearrangement Edit Distance Input String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Chen, X., Zheng, J., Fu, Z., Nan, P., Zhong, Y., Lonardi, S., Jiang, T.: Computing the assignment of orthologous genes via genome rearrangement. In: Proc. of the 3rd Asia-Pacific Bioinformatics Conf. (APBC 2005), pp. 363–378 (2005)Google Scholar
  2. 2.
    Christie, D.A., Irving, R.W.: Sorting strings by reversals and by transpositions. SIAM Journal on Discrete Mathematics 14(2), 193–206 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chrobak, M., Kolman, P., Sgall, J.: The greedy algorithm for the minimum common string partition problem. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) RANDOM 2004 and APPROX 2004. LNCS, vol. 3122, pp. 84–95. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Damaschke, P.: Minimum Common String Partition Parameterized. In: Crandall, K.A., Lagergren, J. (eds.) WABI 2008. LNCS (LNBI), vol. 5251, pp. 87–98. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  6. 6.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  7. 7.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)zbMATHGoogle Scholar
  8. 8.
    Goldstein, A., Kolman, P., Zheng, J.: Minimum common string partitioning problem: Hardness and approximations. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 473–484. Springer, Heidelberg (2004); also in: The Electronic Journal of Combinatorics 12 (2005), paper R50Google Scholar
  9. 9.
    Kaplan, H., Shafrir, N.: The greedy algorithm for edit distance with moves. Inf. Process. Lett. 97(1), 23–27 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kolman, P., Walen, T.: Reversal Distance for Strings with Duplicates: Linear Time Approximation Using Hitting Set. In: Erlebach, T., Kaklamanis, C. (eds.) WAOA 2006. LNCS, vol. 4368, pp. 279–289. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Kolman, P.: Approximating reversal distance for strings with bounded number of duplicates. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 580–590. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Kolman, P., Walen, T.: Approximating reversal distance for strings with bounded number of duplicates. Discrete Applied Mathematics 155(3), 327–336 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Haitao Jiang
    • 1
    • 2
  • Binhai Zhu
    • 1
  • Daming Zhu
    • 2
  • Hong Zhu
    • 3
  1. 1.Department of Computer ScienceMontana State UniversityBozemanUSA
  2. 2.School of Computer Science and TechnologyShandong UniversityJinanChina
  3. 3.College of SoftwareEast China Normal UniversityShanghaiChina

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