Better Filtering with Gapped q-Grams

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.