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Algorithms 2013, 6(4), 636-677; doi:10.3390/a6040636

Sublinear Time Motif Discovery from Multiple Sequences

* ,
Department of Computer Science, University of Texas-Pan American, 1201 W University Dr., Edinburg, TX 78539, USA
* Author to whom correspondence should be addressed.
Received: 11 June 2013 / Revised: 30 September 2013 / Accepted: 1 October 2013 / Published: 14 October 2013
(This article belongs to the Special Issue Algorithms for Sequence Analysis and Storage)
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In this paper, a natural probabilistic model for motif discovery has been used to experimentally test the quality of motif discovery programs. In this model, there are k background sequences, and each character in a background sequence is a random character from an alphabet, Σ. A motif G = g1g2 ... gm is a string of m characters. In each background sequence is implanted a probabilistically-generated approximate copy of G. For a probabilistically-generated approximate copy b1b2 ... bm of G, every character, bi, is probabilistically generated, such that the probability for bi gi is at most α. We develop two new randomized algorithms and one new deterministic algorithm. They make advancements in the following aspects: (1) The algorithms are much faster than those before. Our algorithms can even run in sublinear time. (2) They can handle any motif pattern. (3) The restriction for the alphabet size is a lower bound of four. This gives them potential applications in practical problems, since gene sequences have an alphabet size of four. (4) All algorithms have rigorous proofs about their performances. The methods developed in this paper have been used in the software implementation. We observed some encouraging results that show improved performance for motif detection compared with other software.
Keywords: motif discovery; sublinear time; randomized algorithm; deterministic algorithm motif discovery; sublinear time; randomized algorithm; deterministic algorithm
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Fu, B.; Fu, Y.; Xue, Y. Sublinear Time Motif Discovery from Multiple Sequences. Algorithms 2013, 6, 636-677.

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