@article{dmtcs/AlbertLLV15-321avoiding,
author    = {Michael H. Albert and
Marie{-}Louise Lackner and
Martin Lackner and
Vincent Vatter},
title       = {The Complexity of Pattern Matching for 321-Avoiding and Skew-Merged Permutations},
url = {http://dmtcs.episciences.org/2607},
journal = {{Discrete Mathematics & Theoretical Computer Science}},
volume = {{vol. 18 no. 2, Permutation Patterns 2015}},
year = {2016},
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 $\tau$.},
}