This invention related to a method for computing the minimum edit distance, measured as the number of insertions plus the number of deletions, between two sequences of data, which runs in an amount of time that is nearly proportional to the size of the input data under many circumstances. Utilizing the A* (or A-star) search, the invention searches for the answer using a novel counting heuristic that gives a lower bound on the minimum edit distance for any given subproblem. In addition, regions over which the heuristic matches the maximum value of the answer are optimized by eliminating the search over redundant paths. The invention can also be used to produce the edit script. The invention can be modified for other types of comparison and pattern recognition.