Approximate string matching using compressed suffix arrays

Let T be a text of length n and P be a pattern of length m, both strings over a fixed finite alphabet A. The k-difference (k-mismatch, respectively) problem is to find all occurrences of P in T that have edit distance (Hamming distance, respectively) at most k from P. In this paper we investigate a well-studied case in which T is fixed and preprocessed into an indexing data structure so that any pattern query can be answered faster. We give a solution using an O(nlogn) bits indexing data structure with O(|A|kmk·max(k,logn)+occ) query time, where occ is the number of occurrences. The best previous result requires O(nlogn) bits indexing data structure and gives O(|A|kmk+2+occ) query time. Our solution also allows us to exploit compressed suffix arrays to reduce the indexing space to O(n) bits, while increasing the query time by an O(logn) factor only.