Splaying Preorders and Postorders

@article{Levy2019SplayingPA,
  title={Splaying Preorders and Postorders},
  author={Caleb C. Levy and Robert Endre Tarjan},
  journal={ArXiv},
  year={2019},
  volume={abs/1907.06309}
}
Let $T$ be a binary search tree. We prove two results about the behavior of the Splay algorithm (Sleator and Tarjan 1985). Our first result is that inserting keys into an empty binary search tree via splaying in the order of either $T$'s preorder or $T$'s postorder takes linear time. Our proof uses the fact that preorders and postorders are pattern-avoiding: i.e. they contain no subsequences that are order-isomorphic to $(2,3,1)$ and $(3,1,2)$, respectively. Pattern-avoidance implies certain… 

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