贪心二叉搜索树具有非平凡的竞争力
The Greedy Binary Search Tree is Non-trivially Competitive
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中文总结 AI 辅助
本研究证明$\textsf{Greedy}$二叉搜索树的竞争力为$2^{O(\root{}\root{}\text{log log }n)}$，采用缩放方法结合Wilber交错下界展开分析，为其$O(1)$竞争力的推测提供了非平凡的进展。
中文摘要 AI 辅助
我们证明了$\textsf{Greedy}$二叉搜索树的竞争力为$2^{O(\root{}\root{}\text{log log }n)}$。学界普遍推测$\textsf{Greedy}$的竞争力为$O(1)$，但在此项工作之前，对于任何非平凡的$f(n)=o(\text{log }n)$，都不清楚它是否具备$f$-竞争力。我们的分析不同于此前二叉搜索树的分析，采用了可称为“缩放”的方法，即精细尺度下的代价与粗糙尺度下的代价相关联，并结合Wilber的交错下界。
英文摘要
We prove that the $\textsf{Greedy}$ binary search tree is $2^{O(\sqrt{\log\log n})}$-competitive. It is widely conjectured that $\textsf{Greedy}$ is $O(1)$-competitive, but before this work it was not known to be $f$-competitive, for any non-trivial $f(n)=o(\log n)$. Our analysis differs from prior analyses of binary search trees. It takes what might be called a "scaling" approach, where the cost at a refined scale is related to the cost at a coarser scale, and Wilber's interleave lower bound.
