Constant-Time Randomized Parallel String Matching

Given a pattern string of length m for the string-matching problem, we design an algorithm that computes deterministic samples of a sufficiently long substring of the pattern in constant time. This problem used to be the bottleneck in the pattern preprocessing for one- and two-dimensional pattern ma...

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Vydáno v:SIAM journal on computing Ročník 26; číslo 4; s. 950 - 960
Hlavní autoři: Crochemore, Maxime, Galil, Zvi, Gasieniec, Leszek, Park, Kunsoo, Rytter, Wojciech
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Society for Industrial and Applied Mathematics 01.08.1997
Témata:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Artificial intelligence
Candidates
Codes
Computer Science
Computer science; control theory; systems
Data Structures and Algorithms
Exact sciences and technology
Language theory and syntactical analysis
Pattern recognition. Digital image processing. Computational geometry
Theoretical computing
Randomization
Optimal algorithm
Parallel algorithms
Pattern matching
ISSN:0097-5397, 1095-7111
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Shrnutí:Given a pattern string of length m for the string-matching problem, we design an algorithm that computes deterministic samples of a sufficiently long substring of the pattern in constant time. This problem used to be the bottleneck in the pattern preprocessing for one- and two-dimensional pattern matching. The best previous time bound was O(log2m / log log m). We use this algorithm to obtain the following results (all algorithms below are optimal parallel algorithms on a CRCW PRAM): a deterministic string-matching algorithm which takes O(log log m) time for preprocessing and constant time for text search, which are the best possible in both preprocessing and text search; a constant-time deterministic string-matching algorithm in the case where the text length n satisfies $n=\Omega(m^{1+\epsilon})$ for a constant $\epsilon > 0$; a simple string-matching algorithm that has constant time with high probability for random input; the main result: a constant-expected-time Las Vegas algorithm for computing the period of the pattern and all witnesses and thus for string matching itself; in both cases, an $\Omega(\log\log m)$ lower bound is known for deterministic algorithms.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0097-5397
1095-7111
DOI:10.1137/S009753979528007X