• DOI:10.1137/S009753979528007X
• Corpus ID: 17381189

Constant-Time Randomized Parallel String Matching

@article{Crochemore1997ConstantTimeRP,
  title={Constant-Time Randomized Parallel String Matching},
  author={Maxime Crochemore and Zvi Galil and Leszek Gąsieniec and Kunsoo Park and Wojciech Rytter},
  journal={SIAM J. Comput.},
  year={1997},
  volume={26},
  pages={950-960}
}

• M. Crochemore, Z. Galil, +2 authors W. Rytter
• Published 1 August 1997
• Computer Science
• SIAM J. Comput.

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(log2 m / 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.