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arXiv · 2608.04410

The Greedy Binary Search Tree is Non-trivially Competitive

Yuhao Guo·Seth Pettie·Daniel Skora·Chengzhang Wan
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Abstract

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.

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Yuhao Guo, Seth Pettie, Daniel Skora, Chengzhang Wan. 2026-08-05. The Greedy Binary Search Tree is Non-trivially Competitive. https://arxiv.org/abs/2608.04410

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