A Constant Time Optimal Parallel Algorithm for Two-dimensional Pattern Matching

Maxime Crochemore, Leszek Gasieniec, Ramesh Hariharan, S. Muthukrishnan, Wojciech Rytter

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We give an alphabet-independent deterministic parallel algorithm for finding all occurrences of a pattern array of size mh × mw in a text array of size nh × nw in the concurrentread-concurrent-write-parallel-random-access-machine (CRCW-PRAM) model. Our algorithm runs in O(1) time performing optimal, that is, O(nh × nw) work, following preprocessing of the pattern. This improves the previous best bound of O(log log m) time with optimal work [A. Amir, G. Benson, and M. Farach, Proceedings 5th Annual ACM Symposium on Parallel Algorithms and Architectures, ACM, New York, 1993, pp. 79-85], following preprocessing of the pattern, where m = max{mh, mw}. The preprocessing required by our algorithm (and that due to Amir, Benson, and Farach) can be accomplished in O(log log m) time and O(mh × mw) work [M. Crochemore et al., manuscript, 1993], [R. Cole et al., manuscript, 1993].

Original languageEnglish (US)
Pages (from-to)668-681
Number of pages14
JournalSIAM Journal on Computing
Issue number3
StatePublished - Jan 1 1998
Externally publishedYes


  • Duelling
  • Pattern matching
  • Periodicity
  • PRAM
  • Two-dimensional
  • Witnesses

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)


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