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arXiv · 1510.06051

The Complexity of Pattern Matching for $321$-Avoiding and Skew-Merged Permutations

Michael H. Albert·Marie-Louise Lackner·Martin Lackner·Vincent Vatter
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Abstract

The Permutation Pattern Matching problem, asking whether a pattern permutation $\pi$ is contained in a permutation $\tau$, is known to be NP-complete. In this paper we present two polynomial time algorithms for special cases. The first algorithm is applicable if both $\pi$ and $\tau$ are $321$-avoiding; the second is applicable if $\pi$ and $\tau$ are skew-merged. Both algorithms have a runtime of $O(kn)$, where $k$ is the length of $\pi$ and $n$ the length of $\tau$.

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Michael H. Albert, Marie-Louise Lackner, Martin Lackner, Vincent Vatter. 2015-10-20. The Complexity of Pattern Matching for $321$-Avoiding and Skew-Merged Permutations. https://doi.org/10.46298/dmtcs.1308

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