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Journal Article

Better Filtering with Gapped q-Grams


Burkhardt,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Kärkkäinen,  Juha
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Burkhardt, S., & Kärkkäinen, J. (2003). Better Filtering with Gapped q-Grams. Fundamenta Informaticae, 56, 51-70.

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A popular and well-studied class of filters for approximate string matching compares substrings of length $q$, \emph{the $q$-grams}, in the pattern and the text to identify text areas that contain potential matches. A generalization of the method that uses {\em gapped} $q$-grams instead of contiguous substrings is mentioned a few times in literature but has never been analyzed in any depth. In this paper, we report the first results of a study on gapped $q$-grams. We show that gapped $q$-grams can provide orders of magnitude faster and/or more efficient filtering than contiguous $q$-grams. To achieve these results the arrangement of the gaps in the $q$-gram and a filter parameter called \emph{threshold} have to be optimized. Both of these tasks are nontrivial combinatorial optimization problems for which we present efficient solutions. We concentrate on the $k$~mismatches problem, i.e, approximate string matching with the Hamming distance.