A lower bound for the edit-distance problem under an arbitrary cost function

Abstract

The edit distance of two strings is the minimum cost to transform one string into the other by a sequence of deletions, insertions, and replacements. We show that any algorithm that can compute the edit distance of two strings under an arbitrary cost function must take time proportional to n 2 under the RAM model of computation, where n is the length of the strings. As a corollary, we observe that the Hunt-Szymanski algorithm for longest common subsequences cannot be extended to solve the general edit-distance problem.