Motif Matching Using Gapped Patterns

We present new algorithms for the problem of multiple string matching of gapped patterns, where a gapped pattern is a sequence of strings such that there is a gap of fixed length between each two consecutive strings. The problem has applications in the discovery of transcription factor binding sites in DNA sequences when using generalized versions of the Position Weight Matrix model to describe transcription factor specificities. We present a simple practical algorithm, based on bit-parallelism, that, given a text of length n, runs in time O(n(log σ + gw-spandk-len(P)/we) + occ), where occ is the number of occurrences of the patterns in the text, k-len(P) is the total number of strings in the patterns and 1 ≤ gw-span ≤ w is the maximum number of distinct gap lengths that span a single word of w bits in our encoding. We then show how to improve the time complexity to O(n(log σ + log gsize(P)dk-len(P)/we) + occ) in the worst-case, where gsize(P) is the size of the variation range of the gap lengths. Finally, by parallelizing in a different order we obtain O(dn/welen(P)+n+occ) time, where len(P) is the total number of alphabet symbols in the patterns. We also provide experimental results which show that the presented algorithms are fast in practice, and preferable if all the strings in the patterns have unit-length.