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 cāā„ā2. 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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. 363ā378 (2005)
Christie, D.A., Irving, R.W.: Sorting strings by reversals and by transpositions. SIAM Journal on Discrete Mathematics 14(2), 193ā206 (2001)
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. 84ā95. Springer, Heidelberg (2004)
Damaschke, P.: Minimum Common String Partition Parameterized. In: Crandall, K.A., Lagergren, J. (eds.) WABI 2008. LNCS (LNBI), vol. 5251, pp. 87ā98. Springer, Heidelberg (2008)
Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
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. 473ā484. Springer, Heidelberg (2004); also in: The Electronic Journal of Combinatorics 12 (2005), paper R50
Kaplan, H., Shafrir, N.: The greedy algorithm for edit distance with moves. Inf. Process. Lett. 97(1), 23ā27 (2006)
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. 279ā289. Springer, Heidelberg (2007)
Kolman, P.: Approximating reversal distance for strings with bounded number of duplicates. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 580ā590. Springer, Heidelberg (2005)
Kolman, P., Walen, T.: Approximating reversal distance for strings with bounded number of duplicates. Discrete Applied Mathematics 155(3), 327ā336 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jiang, H., Zhu, B., Zhu, D., Zhu, H. (2010). Minimum Common String Partition Revisited. In: Lee, DT., Chen, D.Z., Ying, S. (eds) Frontiers in Algorithmics. FAW 2010. Lecture Notes in Computer Science, vol 6213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14553-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-14553-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14552-0
Online ISBN: 978-3-642-14553-7
eBook Packages: Computer ScienceComputer Science (R0)