A Refined Analysis of the Sequential Access Theorem for Splay Trees

Abstract

A splay tree is a self-adjusting binary search tree that allows access, insertion, and deletion to be performed in amortized $O(\log n)$ time, where $n$ is the number of stored elements. The sequential access theorem states that, when the elements of a splay tree are accessed in increasing order, the amortized cost per operation becomes a constant. In this paper, we show that the upper bound for this constant is at most $5.5$ by refining the existing analysis and introducing a new potential function. Furthermore, we complement our result by showing that there exists a splay tree for which the constant is lower-bounded by almost $4$.