Fast string matching with k-differences

Consider the string matching problem where differences between characters of the pattern and characters of the text are allowed. Each difference is due to either a mismatch between a character of the text and a character of the pattern or a superfluous character in the text or a superfluous character in the pattern. Given a text of length n , a pattern of length m , and an integer k , we present an algorithm for finding all occurrences of the pattern in the text, each with at most k differences. It runs in O ( m + nk 2 ) time for an alphabet whose size is fixed. For general input the algorithm requires O ( m log m + nk 2 ) time. In both cases the space requirement is O ( m ).