Work

Splay trees are almost dynamically optimal

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.18498

Authors: Chmel, Petr, Haeupler, Bernhard, Hladík, Richard, Koucký, Michal, Roeyskoe, Antti, Rozhoň, Václav, Sladký, Ondřej, Tarjan, Robert E.

Institutions: Charles University, ETH Zurich, Sofia University "St. Kliment Ohridski", Princeton University

Topic: Algorithms and Data Compression

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: European Commission

OpenAlex ID: W7170053082

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