Approximate pattern matching in LZ77-compressed texts

Abstract

Suppose we want to support approximate pattern matching in a text $T[1..n]$ whose LZ77 parse consists of z phrases. In this paper we show how, given that parse, we can preprocess T in $\mathcal{O}(z\log n)$ time and space such that later, given a pattern $P[1..m]$ and an edit distance k, we can perform approximate pattern matching in $\mathcal{O}(z\min (mk,m+k^4)+\mathit{occ})$ time and $\mathcal{O}(z\log n+m+\mathit{occ})$ space, where occ is the size of the output.