Abstract
Most research on the edit distance problem and thek-differences problem considered the set of edit operations consisting of changes, insertions, and deletions. In this paper we include theswapoperation that interchanges two adjacent characters into the set of allowable edit operations, and we present anO(tmin(m,n))-time algorithm for the extended edit distance problem, wheretis the edit distance between the given strings, and anO(kn)-time algorithm for the extendedk-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, insertions, and deletions for the edit distance andk-differences problems.
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