Improved Approximate String Matching and Regular Expression Matching on   Ziv-Lempel Compressed Texts
  We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck. 
Philip Bille, Rolf Fagerberg, Inge Li Goertz