Dictionary Compression on the PRAM

Parallel algorithms for lossless data compression via dictionary compression using optimal, longest fragment first (LFF), and greedy parsing strategies are described. Dictionary compression removes redundancy by replacing substrings of the input by references to strings stored in a dictionary. Given a static dictionary stored as a suffix tree, we present a CREW PRAM algorithm for optimal compression which runs in O(M + log M log n) time with O(nM2) processors, where it is assumed that M is the maximum length of any dictionary entry. Under the same model, we give an algorithm for LFF compression which runs in O( log 2 n) time with O(n/ log n) processors where it is assumed that the maximum dictionary entry is of length O( log n). We also describe an O(M + log n) time and O(n) processor algorithm for greedy parsing given a static or sliding-window dictionary. For sliding-window compression, a different approach finds the greedy parsing in O( log n) time using (O(nM log M/ log n) processors. Our algorithms are practical in the sense that their analysis elicits small constants.