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Algorithms for testing occurrences of length 4 patterns in permutations

Author

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  • Yijie Han

    (University of Missouri at Kansas City)

  • Sanjeev Saxena

    (Indian Institute of Technology)

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 $$O(n\log n)$$ O ( n log n ) time. Our parallel algorithms can be implemented in $$O(\log n)$$ O ( log n ) time with $$n/\log n$$ n / log n processors on the CREW PRAM model, or alternatively in $$O(\log \log \log n)$$ O ( log log log n ) time with $$n/\log \log \log n$$ n / log log log n processors on a CRCW PRAM PRAM model. Parallel algorithm can also be implemented in constant time with $$n\log ^3 n$$ 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 $$O(\log n)$$ O ( log n ) time with n processors on the CREW PRAM model.

Suggested Citation

  • Yijie Han & Sanjeev Saxena, 2018. "Algorithms for testing occurrences of length 4 patterns in permutations," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 189-208, January.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:1:d:10.1007_s10878-017-0163-8
    DOI: 10.1007/s10878-017-0163-8
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