Improved Approximate String Matching Using Compressed Suffix Data Structures

Abstract Approximate string matching is about finding a given string pattern in a text by allowing some degree of errors. In this paper we present a space efficient data structure to solve the 1-mismatch and 1-difference problems. Given a text T of length n over an alphabet A, we can preprocess T and give an $O(n\sqrt{\log n}\log |A|)$ -bit space data structure so that, for any query pattern P of length m, we can find all 1-mismatch (or 1-difference) occurrences of P in O(|A|mlog log n+occ) time, where occ is the number of occurrences. This is the fastest known query time given that the space of the data structure is o(nlog 2n) bits. The space of our data structure can be further reduced to O(nlog |A|) with the query time increasing by a factor of log εn, for 0<ε≤1. Furthermore, our solution can be generalized to solve the k-mismatch (and the k-difference) problem in O(|A|kmk(k+log log n)+occ) and O(log εn(|A|kmk(k+log log n)+occ)) time using an $O(n\sqrt{\log n}\log |A|)$ -bit and an O(nlog |A|)-bit indexing data structures, respectively. We assume that the alphabet size |A| is bounded by $O(2^{\sqrt{\log n}})$ for the $O(n\sqrt{\log n}\log |A|)$ -bit space data structure.