Improved approximate string matching using compressed suffix data structures

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 a fixed alphabet A, we can preprocess T and give an O(n root log n)-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(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) if we can afford a slow down factor of log(epsilon) n, for 0 < epsilon <= 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(epsilon) n(\A\(k)m(k)(k + log log n) + occ)) query time using an O(n root log n)-bit and an O(n)-bit indexing data structures, respectively.