Levenshtein Distance Algorithm better than O(n*m)?

Question

I have been looking for an advanced levenshtein distance algorithm, and the best I have found so far is O(n*m) where n and m are the lengths of the two strings. The reason w

Answer 1

If you only want the threshold function - eg, to test if the distance is under a certain threshold - you can reduce the time and space complexity by only calculating the n values either side of the main diagonal in the array. You can also use Levenshtein Automata to evaluate many words against a single base word in O(n) time - and the construction of the automatons can be done in O(m) time, too.