## Optimal Parallel Dictionary Matching and Compression (Extended Abstract) (1995)

Venue: | 7th Annual ACM Symposium on Parallel Algorithms and Architectures |

Citations: | 6 - 3 self |

### BibTeX

@INPROCEEDINGS{Farach95optimalparallel,

author = {Martin Farach and S. Muthukrishnan},

title = {Optimal Parallel Dictionary Matching and Compression (Extended Abstract)},

booktitle = {7th Annual ACM Symposium on Parallel Algorithms and Architectures},

year = {1995},

pages = {244--253}

}

### Years of Citing Articles

### OpenURL

### Abstract

) Martin Farach S. Muthukrishnan y Rutgers University DIMACS April 26, 1995 Abstract Emerging applications in multi-media and the Human Genome Project require storage and searching of large databases of strings -- a task for which parallelism seems the only hope. In this paper, we consider the parallelism in some of the fundamental problems in compressing strings and in matching large dictionaries of patterns against texts. We present the first work-optimal algorithms for these well-studied problems including the classical dictionary matching problem, optimal compression with a static dictionary and the universal data compression with dynamic dictionary of Lempel and Ziv. All our algorithms are randomized and they are of the Las Vegas type. Furthermore, they are fast, working in time logarithmic in the input size. Additionally, our algorithms seem suitable for a distributed implementation. 1 Introduction Large data bases of strings from multi-media applications and the Human G...

### Citations

1259 | A universal algorithm for sequential data compression
- Ziv, Lempel
- 1977
(Show Context)
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679 |
Fast Pattern Matching in Strings
- Knuth, Morris, et al.
- 1977
(Show Context)
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408 |
Some complexity questions related to distributive computing
- Yao
- 1979
(Show Context)
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- Karp, Rabin
- 1987
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295 |
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- 1990
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256 |
On the complexity of finite sequences
- Lempel, Ziv
- 1976
(Show Context)
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208 |
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- Boas, Kaas, et al.
- 1977
(Show Context)
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165 |
Data Compression Methods and Theory
- Storer
- 1988
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- Gazit
- 1991
(Show Context)
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Efficient string matching
- Aho, Corasick
- 1975
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Highly parallelizable problems
- Berkman, Breslauer, et al.
- 1989
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Optimal parallel pattern matching in strings
- VISHKIN
- 1985
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- 1991
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