Fast algorithms for approximately counting mismatches
Information Processing Letters
Randomized algorithms
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Finding similar regions in many strings
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Efficient approximation algorithms for the Hamming center problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On the closest string and substring problems
Journal of the ACM (JACM)
Combinatorial Approaches to Finding Subtle Signals in DNA Sequences
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Distinguishing string selection problems
Information and Computation
Probabilistic Analysis of a Motif Discovery Algorithm for Multiple Sequences
SIAM Journal on Discrete Mathematics
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We study a natural probabilistic model for motif discovery. 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. Each background sequence is implanted with a probabilistically generated approximate copy of G. For a probabilistically generated approximate copy b1b2… bm of G, every character is probabilistically generated such that the probability for bi&neq; gi is at most α. In this article, we develop an efficient algorithm that can discover a hidden motif from a set of sequences for any alphabet Σ with |Σ|≥ 2 and is applicable to DNA motif discovery. We prove that for α c0, &epsis;, and δ2 such that if there are at least c0 log n input sequences, then in O(n2/h(log n)O(1)) time this algorithm finds the motif with probability at least 3/4 for every G∈ Σρ-Ψρ, h,&epsis;(Σ), where n the length of longest sequences, ρ is the length of the motif, h is a parameter with ρ≥ 4h≥ δ2log n, and Ψρ, h,&epsis;(Σ) is a small subset of at most 2−Θ(&epsis;2 h) fraction of the sequences in Σρ.