AI 中文总结
研究伸展树是否动态最优的问题，通过证明得出伸展树具有 \(O(\log\log n \cdot \log^2\log\log n)=\tilde{O}(\log\log n)\) 竞争比，解决了四十年来未知 \(o(\log n)\) 竞争比的问题。
AI 中文摘要
斯利托和塔尔扬在1985年推测伸展树是动态最优的，即在每个访问序列上，其性能在最优离线动态二叉搜索树的常数因子范围内。尽管经过四十年研究，未知有 \(o(\log n)\) 竞争比。本文证明伸展树具有 \(O(\log\log n \cdot \log^2\log\log n)=\tilde{O}(\log\log n)\) 竞争比。
英文摘要
Sleator and Tarjan [JACM, 1985] conjectured that splay trees are dynamically optimal -- that on every access sequence, they perform within a constant factor of the optimal offline dynamic binary search tree. Despite four decades of work, no $o(\log n)$ competitive ratio was known. We prove that splay trees are $O(\log\log n \cdot \log^2\log\log n)=\tilde{O}(\log\log n)$-competitive.
