Abstract
We present sharper upper and lower bounds for a known polynomial-time approximation scheme due to Li, Ma and Wang [7] for the Consensus-Pattern problem. This NP-hard problem is an abstraction of motif finding, a common bioinformatics discovery task. The PTAS due to Li et al. is simple, and a preliminary implementation [8] gave reasonable results in practice. However, the previously known bounds on its performance are useless when runtimes are actually manageable. Here, we present much sharper lower and upper bounds on the performance of this algorithm that partially explain why its behavior is so much better in practice than what was previously predicted in theory. We also give specific examples of instances of the problem for which the PTAS performs poorly in practice, and show that the asymptotic performance bound given in the original proof matches the behaviour of a simple variant of the algorithm on a particularly bad instance of the problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bailey, T.L., Elkan, C.: Fitting a mixture model by expectation maximization to discover motifs in biopolymers. In: Proceedings of the 2nd International Conference on Intelligent Systems for Molecular Biology (ISMB 1994), pp. 28–36. AAAI Press, Menlo Park (1994)
Buhler, J., Tompa, M.: Finding motifs using random projections. In: Proceedings of the 5th Annual International Conference on Computational Molecular Biology (RECOMB 2001), pp. 69–76 (2001)
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)
Keich, U., Pevzner, P.A.: Finding motifs in the twilight zone. Bioinformatics 18, 1374–1381 (2002)
Keich, U., Pevzner, P.A.: Subtle motifs: defining the limits of motif finding algorithms. Bioinformatics 18, 1382–1390 (2002)
Lawrence, C.E., Altschul, S.F., Boguski, M.S., Liu, J.S., Neuwald, A.F., Wootton, J.C.: Detecting subtle sequence signals: a Gibbs sampling strategy for multiple alignment. Science 262(5131), 208–214 (1993)
Li, M., Ma, B., Wang, L.: Finding similar regions in many strings. Journal of Computer and System Sciences 65(1), 73–96 (2002)
Liang, C.: COPIA: A New Software for Finding Consensus Patterns in Unaligned Protein Sequences. Master’s thesis, University of Waterloo (October 2001)
Liu, J.: A Combinatorial Approach for Motif Discovery in Unaligned DNA Sequences. Master’s thesis, University of Waterloo (March 2004)
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)
Thompson, M.E.: Theory of Sample Surveys. Chapman and Hall, Boca Raton (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brejová, B., Brown, D.G., Harrower, I.M., López-Ortiz, A., Vinař, T. (2005). Sharper Upper and Lower Bounds for an Approximation Scheme for Consensus-Pattern . In: Apostolico, A., Crochemore, M., Park, K. (eds) Combinatorial Pattern Matching. CPM 2005. Lecture Notes in Computer Science, vol 3537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496656_1
Download citation
DOI: https://doi.org/10.1007/11496656_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26201-5
Online ISBN: 978-3-540-31562-9
eBook Packages: Computer ScienceComputer Science (R0)