### Approximate String Matching on Ziv-Lempel Compressed Text

#### Juha Kärkkäinen, Gonzalo Navarro and Esko Ukkonen

We present the first nontrivial algorithm for approximate pattern matching on compressed text. The format we choose is the Ziv-Lempel family. Given a text of length u compressed into length n, and a pattern of length m, we report all the R occurrences of the pattern in the text allowing up to k insertions, deletions and substitutions. On LZ78/LZW we need O(mkn + R) time in the worst case and O(k^2n + mk\min(n,(ms)^k) + R) on average where s is the alphabet size. The experimental results show a practical speedup over the basic approach of up to 2X for moderate m and small k. We extend the algorithms to more general compression formats and approximate matching models.