New Bounds for Motif Finding in Strong Instances
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.
Unable to display preview. Download preview PDF.
- 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.Liu, J.: A combinatorial approach for motif discovery in unaligned DNA sequences. Master’s thesis, University of Waterloo (March 2004)Google Scholar
- 7.McDiarmid, C.: Concentration. In: Habib, M. (ed.) Probabilistic methods for algorithmic discrete mathematics, pp. 195–248. Springer, Heidelberg (1998)Google Scholar
- 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