Surprises in approximating Levenshtein distances
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The Levenshtein distance is an important tool for the comparison of symbolic sequences, with many appearances in genome research, linguistics and other areas. For efficient applications, an approximation by a distance of smaller computational complexity is highly desirable. However, our comparison of the Levenshtein with a generic dictionary-based distance indicates their statistical independence. This suggests that a simplification along this line might not be possible without restricting the class of sequences. Several other probabilistic properties are briefly discussed, emphasizing various questions that deserve further investigation.
7 pages, 4 figures; revised version
7 pages, 4 figures; revised version