A parallel algorithm for the fixed-length approximate string matching problem for high throughput sequencing technologies

The approximate string matching problem is to find all locations at which a query of length m matches a substring of a text of length n with k-or-fewer differences. Nowadays, with the advent of novel high throughput sequencing technologies, the approximate string matching algorithms are used to identify similarities, molecular functions and abnormalities in DNA sequences. We consider a generalization of this problem, the fixed-length approximate string matching problem: given a text t, a pattern ρ and an integer ℓ, compute the optimal alignment of all substrings of ρ of length ℓ and a substring of t. We present a practical parallel algorithm of comparable simplicity that requires only time, where w is the word size of the machine (e.g. 32 or 64 in practice) and p the number of processors, by virtue of computing a bit representation of the relocatable dynamic programming matrix for the problem. Thus the algorithm's performance is independent of k and the alphabet size |Σ|.