Algorithm to find edit distance to all substrings

Question

Given 2 strings s and t. I need to find for each substring in s edit distance(Levenshtein distance) to t. Actually I need to

Answer 1

The Wagner-Fischer algorithm gives you the answer for all prefixes "for free".

http://en.wikipedia.org/wiki/Wagner%E2%80%93Fischer_algorithm

The last row of the Wagner-Fischer matrix contains the edit distance from each prefix of s to t.

So as a first crack at your problem, for each i, run Wagner-Fischer and select the smallest element in the last row.

I will be curious to see if anyone else knows (or can find) a better approach.