Sequence comparison on the connection machine

We give two parallel algorithms for sequence comparison on the Connection Machine 2 (CM-2). The specific comparison measure we compute is the edit distance: given a finite alphabet ∑ and two input sequences X ϵ ∑+ and Y ϵ ∑+ the edit distance d(X,Y) is the minimum cost of transforming X into Y via a series of weighted insertions, deletions and substitutions of characters. The edit distance comparison measure is equivalent to or subsumes a broad range of well known sequence comparison measures. The CM-2 is very fast at performing parallel prefix operations. Our contribution consists of casting the problem in terms of these operations. Our first algorithm computes d(X,Y) using N processors and O(M S) time units, where M = min(|X|,||Y|) + 1, N = max(|X|,|Y|) + 1 and S is the time required for a parallel prefix operation. The second algorithm computes d(X,Y) using NM processors and O((log N log M)(S + R)) time units, where R is the time for a ‘router’ communication step—one in which each processor is able to read data, in parallel, from the memory of any other processor. Our algorithms can also be applied to several variants of the problem, such as subsequence comparisons, and one—many and many-many comparisons on 'sequence databases'.