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 a fixed alphabet A, we can preprocess T and give an $O(n\sqrt{{\rm log} n})$-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 log² 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^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)) query time using an $O(n\sqrt{{\rm log} n})$-bit and an O(n)-bit indexing data structures, respectively.