An O(NP) Sequence Comparison Algorithm

Let A and B be two sequences of length M and N respectively, where without loss of generality N ≥ M, and let D be the length of a shortest edit script between them. A parameter related to D is the number of deletions in such a script, P = D/2 − (N − M)/2. We present an algorithm for finding a shortest edit distance of A and B whose worst case running time is O(NP) and whose expected running time is O(N + PD). The algorithm is simple and is very efficient whenever A is similar to a subsequence of B. It is nearly twice as fast as the O(ND) algorithm of Myers [9], and much more efficient when A and B differ substantially in length.