# 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}
}
• Published 15 July 2019
• Computer Science
• ArXiv
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…
4 Citations
• Computer Science
• 2019
It is proved that a lower bound on optimal execution cost is approximately monotone and details how to adapt this proof from the lower bound to Splay, and how to overcome the remaining barriers to establishing dynamic optimality.
• Computer Science
SODA
• 2022
It is shown that a $(1 + \frac{1}{t})-approximation of an optimal size-$n STT for a given search distribution can be computed in time, and a broad family of STTs with linear rotation-distance is identified, allowing the generalization of Splay trees to the STT setting.
• Computer Science
ArXiv
• 2019
This work attempts to lay the foundations for a proof of the dynamic optimality conjecture, which is that the cost of splaying is always within a constant factor of the optimal algorithm for performing searches.
• Computer Science
ArXiv
• 2022
New bounds on the cost of Greedy in the “pattern avoidance” regime are proved and are proved to be within O ( 1 ) factor of the ofﬂine optimal.

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This work attempts to lay the foundations for a proof of the dynamic optimality conjecture, which is that the cost of splaying is always within a constant factor of the optimal algorithm for performing searches.
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