Faster Approximate Pattern Matching in Compressed Repetitive Texts

Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the underlying string(s). Bille et al. (2011) recently showed how, given a straight-line program with r rules for a string s of length n, we can build an O(r)-word data structure that allows us to extract any substring of length m in O(log n + m) time. They also showed how, given a pattern p of length m and an edit distance k ≤ m, their data structure supports finding all occ approximate matches to p in s in O ( r(min(mk, k + m) + log n) + occ ) time. Rytter (2003) and Charikar et al. (2005) showed that r is always at least the number z of phrases in the LZ77 parse of s, and gave algorithms for building straight-line programs with O(z log n) rules. In this paper we give a simple O(z log n)-word data structure that takes the same time for substring extraction but only O ( z min(mk, k + m) + occ ) time for approximate pattern matching.