A Study on Splay Trees

TL;DR

This paper investigates the dynamic optimality conjecture for splay trees, proposing a reduction to a regular access bound that could facilitate proving their universal efficiency in binary search trees.

Contribution

It introduces a new approach by reducing the dynamic optimality conjecture to a more manageable regular access bound, potentially aiding in its proof.

Findings

Reduction of the dynamic optimality conjecture to a regular access bound

Proposes a plausible approach to prove splay trees' efficiency

Potential pathway to establish dynamic optimality

Abstract

We study the dynamic optimality conjecture, which predicts that splay trees are a form of universally efficient binary search tree, for any access sequence. We reduce this claim to a regular access bound, which seems plausible and might be easier to prove. This approach may be useful to establish dynamic optimality.