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 √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|m log 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(n log 2 n) bits. The space of our data structure can be further reduced to O(n log |A|) with the query time increasing by a factor of log ε n, for 0 < ε ≤ 1. Furthermore, our solution can be generalized to solve the k-mismatch (and the k-difference) problem in O(|A| k m k (k + log log n) + occ) and O(log ε n(|A| k m k (k + log log n) + occ)) time using an O(n √log n log |A|)-bit and an O(n log |A|)-bit indexing data structures, respectively. We assume that the alphabet size |A| is bounded by O(2 √log n) for the O(n√log n log |A|)-bit space data structure. © 2007 Springer Science+Business Media, LLC.