Almost work-optimal pram erew decoders of LZ compressed text

Abstract

We show nearly work-optimal parallel decoding algorithms which run on the PRAM EREW in O(log n) time with O(n/(log n)1/2) processors for text compressed with LZ1 and LZ2 methods, where n is the length of the output string. We also present pseudo work-optimal PRAM EREW decoders for finite window compression and LZ2 compression requiring logarithmic time with O(dn) work, where d is the window size and the alphabet size respectively. Finally, we observe that PRAM EREW decoders requiring O(log n) time and O(n/log n) processors are possible with the non-conservative assumption that the computer word length is O(log2 n) bits.