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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               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  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.