Algorithms for testing occurrences of length 4 patterns in permutations

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.