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(n √ m logm). 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(n √ k log k). We also show an algorithm that solves the above problem in time O((n+ (nk3)/m) log k).  2003 Elsevier Inc. All rights reserved.