An Eecient Uniform-cost Normalized Edit Distance Algorithm

A common model for computing the similarity of two strings X and Y of lengths m, and n respectively with m n, is to transform X into Y through a sequence of edit operations which are of three types: insertion, deletion, and substitution of symbols. The model assumes a given weight function which assigns a non-negative real cost to each of these edit operations. The amortized weight for a given edit sequence is the ratio of the total weight of the sequence to its length, and the minimum of this ratio over all edit sequences is the normalized edit distance between X and Y. Experimental results suggest that for some applications normalized edit distance is better as a similarity measure than ordinary edit distance, which ignores the length of the sequences. Existing algorithms for the computation of normalized edit distance with provable bounds on the complexity require O(mn 2) operations in the worst-case. In this paper we develop an O(mn log n) worst-case algorithm for the normalized edit distance problem for uniform weights. In this case the weight of each edit operation is constant within the same type, except substitutions can have diierent costs depending on whether they are matching or non-matching.