Approximate swap and mismatch edit distance

Authors:
Yair Dombb;Ohad Lipsky;Benny Porat;Ely Porat;Asaf Tsur
Affiliations:
Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel and Bar-Ilan University and Google Inc.;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel
Venue:
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
Year:
2007

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Abstract

There is no known algorithm that solves the general case of the Approximate Edit Distance problem, where the edit operations are: insertion, deletion, mismatch, and swap, in time o(nm), where n is the length of the text and m is the length of the pattern. In the effort to study this problem, the edit operations were analyzed independently. Karloff [10] showed an algorithm that approximates the edit distance problem with only the mismatch operation in time O(1/Ɛ2n log3 m). Amir et. al. [3] showed that if the only edit operations allowed are swap and mismatch, then the exact edit distance problem can be solved in time O(n√m log m). In this paper, we discuss the problem of approximate edit distance with swap and mismatch. We show a randomized O(1/Ɛ3n log n log3 m) time algorithm for the problem. The algorithm guarantees an approximation factor of (1 + Ɛ) with probability of at least 1 - 1/n.