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

I found another optimization that claims to be O(max(m, n)):

http://en.wikibooks.org/wiki/Algorithm_Implementation/Strings/Levenshtein_distance#C

(the second C implementation)