Most efficient way to calculate Levenshtein distance

Question

I just implemented a best match file search algorithm to find the closest match to a string in a dictionary. After profiling my code, I found out that the overwhelming major

Answer 1

I know this is very late but it is relevant to the discussion at hand.

As mentioned by others, if all you want to do is check whether the edit distance between two strings is within some threshold k, you can reduce the time complexity to O(kn). A more precise expression would be O((2k+1)n). You take a strip which spans k cells either side of the diagonal cell (length of strip 2k+1) and compute the values of cells lying on this strip.

Interestingly, there's been an improvement by Li et. al. and this has been further reduced to O((k+1)n).