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New Bounds for Motif Finding in Strong Instances

  • Broňa Brejová
  • Daniel G. Brown
  • Ian M. Harrower
  • Tomáš Vinař
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4009)

Abstract

Many algorithms for motif finding that are commonly used in bioinformatics start by sampling r potential motif occurrences from n input sequences. The motif is derived from these samples and evaluated on all sequences. This approach works extremely well in practice, and is implemented by several programs. Li, Ma and Wang have shown that a simple algorithm of this sort is a polynomial-time approximation scheme. However, in 2005, we showed specific instances of the motif finding problem for which the approximation ratio of a slight variation of this scheme converges to one very slowly as a function of the sample size r, which seemingly contradicts the high performance of sample-based algorithms. Here, we account for the difference by showing that, for a variety of different definitions of “strong” binary motifs, the approximation ratio of sample-based algorithms converges to one exponentially fast in r. We also describe “very strong” motifs, for which the simple sample-based approach always identifies the correct motif, even for modest values of r.

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References

  1. 1.
    Brejova, B., Brown, D.G., Harrower, I.M., Lopez-Ortiz, A., Vinar, T.: Sharper upper and lower bounds for an approximation scheme for Consensus-Pattern. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 1–10. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Hertz, G.Z., Stormo, G.D.: Identifying DNA and protein patterns with statistically significant alignments of multiple sequences. Bioinformatics 15(7-8), 563–577 (1999)CrossRefGoogle Scholar
  3. 3.
    Hoeffding, W.J.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58, 713–721 (1963)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Li, M., Ma, B., Wang, L.: Finding similar regions in many strings. Journal of Computer and System Sciences 65(1), 73–96 (2002)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Liang, C.: COPIA: a new software for finding consensus patterns in unaligned protein sequences. Master’s thesis, University of Waterloo (October 2001)Google Scholar
  6. 6.
    Liu, J.: A combinatorial approach for motif discovery in unaligned DNA sequences. Master’s thesis, University of Waterloo (March 2004)Google Scholar
  7. 7.
    McDiarmid, C.: Concentration. In: Habib, M. (ed.) Probabilistic methods for algorithmic discrete mathematics, pp. 195–248. Springer, Heidelberg (1998)Google Scholar
  8. 8.
    Panconesi, A., Srinivasan, A.: Randomized distributed edge coloring via an extension of the Chernoff-Hoeffding bounds. SIAM Journal on Computing 26, 350–368 (1997)CrossRefMathSciNetMATHGoogle Scholar
  9. 9.
    Pevzner, P.A., Sze, S.: Combinatorial approaches to finding subtle signals in DNA sequences. In: Proceedings of the 8th International Conference on Intelligent Systems for Molecular Biology (ISMB 2000), pp. 269–278 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Broňa Brejová
    • 1
  • Daniel G. Brown
    • 1
  • Ian M. Harrower
    • 1
  • Tomáš Vinař
    • 1
  1. 1.David R. Cheriton School of Computer ScienceUniversity of Waterloo 

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