Approximate String Matching: A Simpler Faster Algorithm

TL;DR: Two algorithms for finding all approximate matches of a pattern in a text, where the edit distance between the pattern and the matching text substring is at most k, are given.

Abstract: We give two algorithms for finding all approximate matches of a pattern in a text, where the edit distance between the pattern and the matching text substring is at most k. The first algorithm, which is quite simple, runs in time $O(\frac{nk^3}{m}+n+m)$ on all patterns except k-break periodic strings (defined later). The second algorithm runs in time $O(\frac{nk^4}{m}+n+m)$ on k-break periodic patterns. The two classes of patterns are easily distinguished in O(m)time.