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arXiv · 2607.18498

Splay trees are almost dynamically optimal

Petr Chmel·Bernhard Haeupler·Richard Hladík·Michal Koucký·Antti Roeyskoe·Václav Rozhoň·Ondřej Sladký·Robert E. Tarjan
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Abstract

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.

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Petr Chmel, Bernhard Haeupler, Richard Hladík, Michal Koucký, Antti Roeyskoe, Václav Rozhoň, Ondřej Sladký, Robert E. Tarjan. 2026-07-20. Splay trees are almost dynamically optimal. https://arxiv.org/abs/2607.18498

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