A linear size index for approximate pattern matching

Abstract

This paper revisits the problem of indexing a text S[1.,n] to support searching substrings in S that match a given pattern P[1..m] with at most k errors. A naive solution either has a worst-case matching time complexity of Ω(m k) or requires Ω(n k) space. Devising a solution with better performance has been a challenge until Cole et al. [5] showed an O(nlog k n)-space index that can support k-error matching in O(m+occ+log k n log log n) time, where occ is the number of occurrences. Motivated by the indexing of DNA, we investigate in this paper the feasibility of devising a linear-size index that still has a time complexity linear in m. In particular, we give an O(n)-apace index that supports k-error matching in O(m + occ+ (log n) k(k+1) log log n) worst-case time. Furthermore, the index can be compressed from O(n) words into O(n) bits with a slight increase in the time complexity. © Springer-Verlag Berlin Heidelberg 2006.