Approximate string matching over Ziv-Lempel compressed text

Abstract

We present a solution to the problem of performing approximate pattern matching on compressed text. The format we choose is the Ziv-Lempel family, specifically the LZ78 and LZW variants. 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, in O(mkn+R) time. The existence problem needs O(mkn) time. We also show that the algorithm can be adapted to run in O(k2n+min(mkn;m2(mfi)k) + R) average time, where fi is the alphabet size. The experimental results show a speedup over the basic approach for moderate m and small k.