Two new algorithms for improving the speed of the LZ77 compression are proposed. One is based on a new hashing algorithm named two-level hashing that enables fast longest match searching from a sliding dictionary, and the other uses suffix sorting. The former is suitable for small dictionaries and it significantly improves the speed of gzip, which uses a naive hashing algorithm. The latter is suitable for large dictionaries which improve compression ratio for large files. We also experiment on the compression ratio and the speed of block sorting compression, which uses suffix sorting in its compression algorithm. The results show that the LZ77 using the two-level hash is suitable for small dictionaries, the LZ77 using suffix sorting is good for large dictionaries when fast decompression speed and efficient use of memory are necessary, and block sorting is good for large dictionaries.

In this paper the performance of the Block Sorting algorithm proposed by Burrows and Wheeler is evaluated theoretically. It is proved that the Block Sorting algorithm is asymptotically optimal for stationary ergodic finite order Markov sources. Our proof is based on the facts that symbols with the same Markov state (or context) in an original data sequence are grouped together in the output sequence obtained by Burrows-Wheeler transform, and the codeword length of each group can be bounded by a function described with the frequencies of symbols included in the group.