Generalized Planted (l, d)-Motif Problem with Negative Set

Finding similar patterns (motifs) in a set of sequences is an important problem in Computational Molecular Biology. Pevzner and Sze [18] defined the planted (l,d)-motif problem as trying to find a lengthl pattern that occurs in each input sequence with at most d substitutions. When d is large, this problem is difficult to solve because the input sequences do not contain enough information on the motif. In this paper, we propose a generalized planted (l,d)-motif problem which considers as input an additional set of sequences without any substring similar to the motif (negative set) as extra information. We analyze the effects of this negative set on the finding of motifs, and define a set of unsolvable problems and another set of most difficult problems, known as “challenging generalized problems”. We develop an algorithm called VANS based on voting and other novel techniques, which can solve the (9,3), (11,4),(15,6) and (20,8)-motif problems which were unsolvable before as well as challenging problems of the planted (l,d)-motif problem such as (9,2), (11,3), (15,5) and (20,7)-motif problems.