Approximate string matching on Ziv–Lempel compressed text

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 kinsertions, deletions and substitutions. On LZ78/LZW we need O(mkn+R) time in the worst case and O(k²n+mkmin(n,(mσ)^k)+R) on average where σ 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.