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(n log^k n)-space index that can support k-error matching in O(m + occ + log^k n loglogn) 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)-space index that supports k-error matching in O(m + occ + (logn)$^{k({\it k}+1)}$ loglogn) 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.