Parallel biological sequence comparison using prefix computations

We present practical parallel algorithms using prefix computations for various problems that arise in pairwise comparison of biological sequences. We consider both constant and affine gap penalty functions, full-sequence and subsequence matching, and space-saving algorithms. The best known sequential algorithms solve these problems in O(mn) time and O(m+n) space, where m and n are the lengths of the two sequences. All the algorithms presented in this paper are time optimal with respect to the best known sequential algorithms and can use O (n/log n) processors where n is the length of the larger sequence. While optimal parallel algorithms for many of these problems are known, we use a simple framework and demonstrate how these problems can be solved systematically using repeated parallel prefix operations. We also present a space-saving algorithm that uses O (m+n/p) space and runs in optimal time where p is the number of the processors used.