Faster Algorithms for String Matching with k Mismatches

The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length m and every length m substring of the text T. Currently, the fastest algorithms for this problem are the following. The Galil–Giancarlo algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in time O(nk). The Abrahamson algorithm finds the number of mismatches at every location in time O(nmlogm). We present an algorithm that is faster than both. Our algorithm finds all locations where the pattern has at most k errors in time O(nklogk). We also show an algorithm that solves the above problem in time O((n+(nk3)/m)logk).