发表机构
Keio University（庆应义塾大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文精细化分析伸展树的顺序访问定理，通过新势函数将摊还成本常数上界改进至5.5，并证明存在下界接近4的实例。
AI 中文摘要
伸展树是一种自调整二叉搜索树，允许在摊还O(log n)时间内完成访问、插入和删除操作，其中n是存储的元素个数。顺序访问定理指出，当伸展树的元素按递增顺序被访问时，每次操作的摊还成本变为常数。在本文中，我们通过改进现有分析并引入新的势函数，证明了该常数的上界至多为5.5。此外，我们通过展示存在一棵伸展树使得该常数下界接近4，来补充我们的结果。
英文摘要
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 $4$.
