Better Filtering with Gapped q-Grams

Issue title: Computing Patterns in Strings

Article type: Research Article

Authors: Burkhardt, Stefan | Kärkkäinen, Juha

Affiliations: Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany

Abstract: A popular and well-studied class of filters for approximate string matching compares substrings of length q, the q-grams, in the pattern and the text to identify text areas that contain potential matches. A generalization of the method that uses 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 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.

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Journal: Fundamenta Informaticae, vol. 56, no. 1-2, pp. 51-70, 2003