Fast Computation of Normalized Edit Distances

The Normalized Edit Distance (NED) between two strings X and Y is defined as the minimum quotient between the sum of weights of the edit operations required to transform X into Y and the length of the editing path corresponding to these operations. An algorithm for computing the NED has recently been introduced by Marzal and Vidal that exhibits O(mn2) computing complexity, where m and n are the lengths of X and Y. We propose here an algorithm that is observed to require in practice the same O(mn) computing resources as the conventional unnormalized Edit Distance algorithm does. The performance of this algorithm is illustrated through computational experiments with synthetic data, as well as with real data consisting of OCR chain-coded strings.