String Matching in the DNA Alphabet

Searching for occurrences of string patterns is a common problem in many applications. Various good solutions have been presented for string matching. The most efficient solutions in practice are based on the Boyer–Moore algorithm.1 A typical question in molecular biology is whether a given sequence has appeared elsewhere. In the following, we will concentrate on searching for exact occurrences of long patterns in the DNA alphabet which in a typical case contains four characters, namely a, c, g, and t. However, the biologists are often interested in finding similar sequences. Nevertheless, exact searching can be used as a fast subroutine of approximate searching. At low error levels any algorithm for exact searching can be used as a fast filtering method. Assume that we allow e errors. If we divide the pattern in e+1 distinct blocks, every approximate occurrence contains an exact occurrence of at least one of the blocks. Thus an occurrence of any block defines a potential approximate occurrence of the pattern, which can be checked with a slower dynamic programming method. Hume and Sunday3 review several techniques how to improve the practical efficiency of the Boyer–Moore algorithm using different shift heuristics, tight loops, unrolling of loops, and some other approaches. Their study mainly deals with searching for words of an English text, but they also tested their algorithms on DNA strings. Later Kim and Shawe-Taylor present more efficient solutions for DNA strings based on an implementation of an algorithm introduced by Baeza-Yates.5 We will introduce a new version of the Baeza-Yates algorithm,4,5 which is a modification of the Boyer–Moore–Horspool algorithm6 for small alphabets. In the Baeza-Yates algorithm the