Abstract

The problem of comparing two sequences A and B to determine their LCS or the edit distance between them has been much studied. In this paper we consider the following incremental version of these problems: given an appropriate encoding of a comparison between A and B, can one incrementally compute the answer for A and bB, and the answer for A and Bb with equal efficiency, where b is an additional symbol? Our main result is a theorem exposing a surprising relationship between the dynamic programming solutions for two such "adjacent" problems. Given a threshold k on the number of differences to be permitted in an alignment, the theorem leads directly to an O(k) algorithm for incrementally computing a new solution from an old one, as contrasts the O(k²) time required to compute a solution from scratch. We further show with a series of applications that this algorithm is indeed more powerful than its non-incremental counterpart by solving the applications with greater asymptotic ef...

Citations