Abstract
While sliding window (LZ1) compression can be parallelized efficiently, the LZ2 compression method seems hardly parallelizable since some related heuristics are known to be P-complete. In spite of such negative result, there are parallel decoders which run in O(log/sup 2/ n) time with O(n/log n) processors on the PRAM EREW where n is the length of the output string, as for LZ1 decompression. We show a faster parallel decoding algorithm which runs on the PRAM EREW in O(log n) time with O(n) processors for text compressed by a standard implementation of the LZ2 algorithm (next character heuristic). We observe that LZ1 parallel decoders also can have such speed up. Moreover, we address a different implementation of LZ2 compression called identity heuristic. In this case, decoding on the PRAM EREW takes O(log n log log n) time with O(n/log n) processors with the realistic assumption that the length of the dictionary elements is logarithmic.
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