Efficient algorithms for approximate string matching with swaps

Most research on the edit distance problem and the k-differences problem considered the set of edit operations consisting of changes, deletions, and insertions. In this paper we include the swap operation that interchanges two adjacent characters into the set of allowable edit operations, and we present an O(t min(m, n))-time algorithm for the extended edit distance problem, where t is the edit distance between the given strings, and an O(kn)-time algorithm for the extended k-differences problem. That is, we add swaps into the set of edit operations without increasing the time complexities of previous algorithms that consider only changes, deletions, and insertions for the edit distance and k-differences problems.