Efficient Exact and Approximate Algorithms for the Complement of Maximal Strip Recovery

  • Binhai Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)


Given two genomic maps G and H represented by a sequence of n gene markers, a strip (syntenic block) is a sequence of distinct markers of length at least two which appear as subsequences in the input maps, either directly or in reversed and negated form. The problem Maximal Strip Recovery (MSR) is to find two subsequences G′ and H′ of G and H, respectively, such that the total length of disjoint strips in G′ and H′ is maximized (i.e., conversely, the complement of the problem CMSR is to minimize the number of markers deleted to have a feasible solution). Recently, both MSR and its complement are shown to be NP-complete. A factor-4 approximation is known for the MSR problem and an FPT algorithm is known for the CMSR problem which runs in O(23.61k n + n 2) time (where k is the minimum number of markers deleted). We show in this paper that there is a factor-3 asymptotic approximation for CMSR and there is an FPT algorithm which runs in O(3 k n + n 2) time for CMSR, significantly improving the previous bound.


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  1. 1.
    Bar-Yehuda, R., Halldórsson, M.M., Naor, J.(S.), Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM Journal on Computing 36, 1–15 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bulteau, L., Fertin, G., Rusu, I.: Maximal strip recovery problem with gaps: hardness and approximation algorithms. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 710–719. Springer, Heidelberg (2009)Google Scholar
  3. 3.
    Butman, A., Hermelin, D., Lewenstein, M., Rawitz, D.: Optimization problems in multiple-interval graphs. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), pp. 268–277 (2007)Google Scholar
  4. 4.
    Chen, Z., Fu, B., Jiang, M., Zhu, B.: On recovering syntenic blocks from comparative maps. Journal of Combinatorial Optimization 18, 307–318 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Choi, V., Zheng, C., Zhu, Q., Sankoff, D.: Algorithms for the extraction of synteny blocks from comparative maps. In: Giancarlo, R., Hannenhalli, S. (eds.) WABI 2007. LNCS (LNBI), vol. 4645, pp. 277–288. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  7. 7.
    Jiang, H., Zhu, B.: Weak kernels. ECCC Report, TR10-005 (May 2010)Google Scholar
  8. 8.
    Jiang, M.: Inapproximability of maximal strip recovery. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 616–625. Springer, Heidelberg (2009)Google Scholar
  9. 9.
    Jiang, M.: Inapproximability of maximal strip recovery, II. In: Proceedings of the 4th Annual Frontiers of Algorithmics Workshop, FAW 2010 (to appear 2010)Google Scholar
  10. 10.
    Vazirani, V.: Approximation Algorithms. Springer, Heidelberg (2001)Google Scholar
  11. 11.
    Wang, L., Zhu, B.: On the tractability of maximal strip recovery. J. of Computational Biology (to appear 2010); An earlier version appeared in TAMC 2009Google Scholar
  12. 12.
    Zheng, C., Zhu, Q., Sankoff, D.: Removing noise and ambiguities from comparative maps in rearrangement analysis. IEEE/ACM Transactions on Computational Biology and Bioinformatics 4, 515–522 (2007)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Binhai Zhu
    • 1
  1. 1.Department of Computer ScienceMontana State UniversityBozemanUSA

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