Relationship With Other Edit Distance Metrics
Levenshtein distance is not the only popular notion of edit distance. Variations can be obtained by changing the set of allowable edit operations: for instance,
- length of the longest common subsequence is the metric obtained by allowing only addition and deletion, not substitution;
- the Damerau–Levenshtein distance allows addition, deletion, substitution, and the transposition of two adjacent characters;
- the Hamming distance only allows substitution (and hence, only applies to strings of the same length).
Edit distance in general is usually defined as a parametrizable metric in which a repertoire of edit operations is available, and each operation is assigned a cost (possibly infinite). This is further generalized by DNA sequence alignment algorithms such as the Smith–Waterman algorithm, which make an operation's cost depend on where it is applied.
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