Algorithms for testing occurrences of length 4 patterns in permutations

Yijie Han () and Sanjeev Saxena ()
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Yijie Han: University of Missouri at Kansas City
Sanjeev Saxena: Indian Institute of Technology

Journal of Combinatorial Optimization, 2018, vol. 35, issue 1, No 15, 189-208

Abstract: 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.

Keywords: Separable permutations; Length 4 permutations; Pattern matching; Optimal algorithms; Parallel algorithms (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0163-8

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