Practical Parallel Algorithms for Dictionary Data Compression

Abstract

PRAM CREW parallel algorithms requiring logarithmic time and a linear number of processors exist for sliding (LZ1) and static dictionary compression. On the other hand, LZ2 compression seems hard to parallelize. Both adaptive methods work with prefix dictionaries, that is, all prefixes of a dictionary element are dictionary elements.Therefore, it is reasonable to use prefix dictionaries also for the static method. A left to right semi-greedy approach exists to compute an optimal parsing of a string with a prefix static dictionary. The left to right greedy approach is enough to achieve optimal compression with a sliding dictionary since such dictionary is both prefix and suffix. We assume the window is bounded by a constant. With the practical assumption that the dictionary elements have constant length we present PRAM EREW algorithms for sliding and static dictionary compression still requiring logarithmic time and a linear number of processors. A PRAM EREW decoder for static dictionary compression can be easily designed with a linear number of processors and logarithmic time. A work-optimal logarithmic time PRAM EREW decoder exists for sliding dictionary compression when the window has constant length. The simplest model for parallel computation is an array of processors with distibuted memory and no interconnections, therefore, no communication cost. An approximation scheme to optimal compression with prefix static dictionaries was designed running with the same complexity of the previous algorithms on such model. It was presented for a massively parallel architecture but in virtue of its scalability it can be implemented on a small scale system as well.We describe such approach and extend it to the sliding dictionary method. The approximation scheme for sliding dictionaries is suitable for small scale systems but due to its adaptiveness it is practical for a large scale system when the file size is large. A two-dimensional extension of the sliding dictionary method to lossless compression of bi-level images, called BLOCK MATCHING, is also discussed. We designed a parallel implementation of such heuristic on a constant size array of processors and experimented it with up to 32 processors of a 256 Intel Xeon 3.06 GHz  processors machine (avogadro.cilea.it) on a test set of large topographic images. We achieved the expected speed-up, obtaining parallel compression and decompression about twenty-five times faster than the sequential ones.