Abstract
In this paper linear time sequential and optimal parallel algorithms for testing pattern involvement for all length 4 permutations are described. This is an improvement as the previous best sequential algorithms, for most of these pattern require \(O(n\log n)\) time. Our parallel algorithms can be implemented in \(O(\log n)\) time with \(n/\log n\) processors on the CREW PRAM model, or alternatively in \(O(\log \log \log n)\) time with \(n/\log \log \log n\) processors on a CRCW PRAM PRAM model. Parallel algorithm can also be implemented in constant time with \(n\log ^3 n\) processors on a CRCW PRAM model. The previous best parallel algorithms were available for only some of these patterns and took \(O(\log n)\) time with n processors on the CREW PRAM model.
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Acknowledgements
We thank anonymous referees for careful reading of the manuscript, and their critical comments and suggestions. We believe these suggestions have helped in improving the manuscript.
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Preliminary version of this paper was published in Y. Han, S. Saxena. Algorithms for testing length four permutations. Proceedings 2013 International Frontiers in Algorithmic Workshop (FAW-AAIM’2013) LNCS 7924, 17–23 and Y. Han, S. Saxena: Parallel Algorithms for Testing Length Four Permutations, International Symposium on Parallel Architectures, Algorithms and Programming (PAAP’2014), 81–86.
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Han, Y., Saxena, S. Algorithms for testing occurrences of length 4 patterns in permutations. J Comb Optim 35, 189–208 (2018). https://doi.org/10.1007/s10878-017-0163-8
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DOI: https://doi.org/10.1007/s10878-017-0163-8