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47-58, 2004. Y. Sun and J. Buhler, “Designing Multiple Simultaneous Seeds for DNA Similarity Search,” Proc. Eighth Ann. Int’l Conf. Computational Biology, pp. 76-84, 2004. D. Kisman, M. Li, B. Ma, and L. Wang, “TPatternHunter: Gapped, Fast and Sensitive Translated Homology Search,” Bioinformatics, 2004. 38 [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS, T. Smith and M. Waterman, “Identification of Common Molecular Subsequences,” J.

This avoids the use of the SmithWaterman algorithm [8] for pairwise local alignment, which has ÂðnmÞ runtimes on input sequences A and B of length n and m, respectively. ) Instead, assuming random sequences, the expected runtime of this heuristic search method is hðn; mÞ þ aðn; mÞ, where hðn; mÞ is the amount of time needed to find hits in the two sequences and aðn; mÞ is the expected time needed to compute the alignments from the hits. Most heuristic aligners have hðn; mÞ ¼ Âðn þ m þ nm=kÞ, while aðn; mÞ ¼ Âðnm=kÞ for some large constant k.

For the input string s 2 ÆÃ with n ¼ jsj, we consider the location list Lx  f0::n À 1g as the set of all the positions on s at which x occurs. When a pattern u occurs in another pattern (or into a string) v, we also say that v contains u. For example, the location list of x ¼ T  G in s ¼ TTGG is Lx ¼ f0; 1g, hence s contains x. Definition 4 (motif). Given a parameter q ! 2, called quorum, we say that pattern x is a motif in s when jLx j ! q. Given any location list Lx and any integer d, we adopt the notation Lx þ d ¼ f‘ þ d j ‘ 2 Lx g for indicating the occurrences in Lx “displaced” by the offset d.

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