Bounded size dictionary compression: SCk-completeness and NC algorithms

Agostino, Sergio De; Silvestri, Riccardo

doi:10.1016/s0890-5401(02)00013-5

Cited by 8 publications

(8 citation statements)

References 19 publications

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“…Much more interesting is what can be said about the parallel complexity analysis. In [7] it was shown that LZ2 (or LZW) compression using the LRU deletion heuristic with a dictionary of size c can be performed in parallel either in O(log n) time with 2 O(c log c) n processors or in 2 O(c log c) log n time with O(n) processors.…”

Section: The Completeness Resultsmentioning

confidence: 99%

“…In [7] a relaxed version (RLRU) was introduced which turned out to be the first (and only so far) natural SC k -complete problem. RLRU partitions the dictionary in p equivalence classes, so that all the elements in each class are considered to have the same "age" for the LRU strategy.…”

Section: The Completeness Resultsmentioning

confidence: 99%

“…Realistically, the satisfaction of these requirements is a necessary but not a sufficient condition for a practical parallel algorithm since the number of processors should be linear, which does not seem possible for the RESTART deletion heuristic. Moreover, the SC k -completeness of LZ2 compression using the LRU deletion heuristic and a dictionary of polylogarithmic size shows that it is unlikely to have a parallel complexity involving reasonable multiplicative constants [7]. In conclusion, the only practical LZW compression algorithm for a shared memory parallel system is the one using the FREEZE deletion heuristic.…”

Section: Lempel-ziv Compression On a Parallel Systemmentioning

confidence: 96%

“…The tree and the path are computed in O(k) time with O(n/k) processors if k is Ω(log n), as in the first subsection without reading and writing conflicts [8]. The parallelization of the sequential LZW compression algorithm with the RESTART deletion heuristic is not practical enough since it requires a quadratic number of processors [7].…”

Section: Lzw Compression On a Parallel Systemmentioning

confidence: 99%

“…This computational difference implies that while LZ1 compression has efficient parallel algorithms [4,5] LZ2 compression is hard to parallelize [6]. This difference is maintained when bounded memory versions of Lempel-Ziv compression are considered [5,7,8]. On the other hand, parallel decompression is possible for both approaches [9].…”

Section: Introductionmentioning

confidence: 99%

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Lempel–Ziv Data Compression on Parallel and Distributed Systems

Agostino

2011

Algorithms

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Section: The Completeness Resultsmentioning

confidence: 99%

Section: The Completeness Resultsmentioning

confidence: 99%

Section: Lempel-ziv Compression On a Parallel Systemmentioning

confidence: 96%

Section: Lzw Compression On a Parallel Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lempel–Ziv Data Compression on Parallel and Distributed Systems

Agostino

2011

Algorithms

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Efficient Rational Proofs for Space Bounded Computations

Campanelli

Gennaro

2017

Lecture Notes in Computer Science

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Scalability and Communication in Parallel Low-Complexity Lossless Compression

2010

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Approximation schemes for optimal compression with static and sliding dictionaries which can run on a simple array of processors with distributed memory and no interconnections are presented. These approximation algorithms can be implemented on both small and large scale parallel systems. The sliding dictionary method requires large size files on large scale systems. As far as lossless image compression is concerned, arithmetic encoders enable the best lossless compressors but they are often ruled out because they are too complex. Storer extended dictionary text compression to bi-level images to avoid arithmetic encoders (BLOCK MATCHING). We were able to partition an image into up to a hundred areas and to apply the BLOCK MATCHING heuristic independently to each area with no loss of compression effectiveness. Therefore, the approach is suitable for a small scale parallel system at no communication cost. On the other hand, bi-level image compression seems to require communication on large scale systems. With regard to grey scale and color images, parallelizable lossless image compression (PALIC) is a highly parallelizable and scalable lossless compressor since it is applied independently to blocks of 8 × 8 pixels. We experimented the BLOCK MATCHING and PALIC heuristics with up to 32 processors of a 256 Intel Xeon 3.06 GHz processors machine (http://avogadro.cilea.it) on a test set of large topographic bi-level images and color images in RGB format. We obtained the expected speed-up of the compression and decompression times, achieving parallel running times about 25 times faster than the sequential ones. Finally, scalable algorithms computing static and sliding dictionary optimal text compression on an exclusive read, exclusive write shared memory parallel machine are presented. On the same model, compression by block matching of bi-level images is shown which can be implemented on a full binary tree architecture under some realistic assumptions with no scalability issues.The work was supported by the Italian Research Project PRIN and preliminary results were presented in [1][2][3].

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Bounded size dictionary compression: SCk-completeness and NC algorithms

Cited by 8 publications

References 19 publications

Lempel–Ziv Data Compression on Parallel and Distributed Systems

Lempel–Ziv Data Compression on Parallel and Distributed Systems

Efficient Rational Proofs for Space Bounded Computations

Scalability and Communication in Parallel Low-Complexity Lossless Compression

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