A Normalized Levenshtein Distance Metric

Although a number of normalized edit distances presented so far may offer good performance in some applications, none of them can be regarded as a genuine metric between strings because they do not satisfy the triangle inequality. Given two strings X and Y over a finite alphabet, this paper defines a new normalized edit distance between X and Y as a simple function of their lengths (|X| and |Y|) and the Generalized Levenshtein Distance (GLD) between them. The new distance can be easily computed through GLD with a complexity of O(|X|.|Y|) and it is a metric valued in [0, 1] under the condition that the weight function is a metric over the set of elementary edit operations with all costs of insertions/deletions…

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  Alliance for Accelerating Excellence in Science in Africa