Dynamic optimality conjecture for splay trees

Establish whether splay trees achieve, up to a constant factor, the performance of the best possible dynamic binary search tree, including one that knows the entire access sequence in advance.

Background

The paper identifies dynamic optimality as a central unresolved question concerning splay trees. The conjecture compares the performance of splay trees with that of an optimal dynamic binary search tree, even when the comparator is given complete advance knowledge of the access sequence. A proof would establish a broad optimality guarantee for splay trees beyond the specific sequential-access bound proved in the paper.

References

A central open question on splay trees is the dynamic optimality conjecture, which states that splay trees achieve, up to a constant factor, the performance of the best possible dynamic binary search tree, even one that knows the whole access sequence in advance.

— A Refined Analysis of the Sequential Access Theorem for Splay Trees  (2609.19746 - Kakimura et al., 17 Sep 2026) in Section 1, subsection “Other Related Work”

The traversal conjecture states that, if we access a splay tree $T$ in the order given by the preorder sequence of another tree $T'$, then the total cost is $O(n)$.

— A Refined Analysis of the Sequential Access Theorem for Splay Trees  (2609.19746 - Kakimura et al., 17 Sep 2026) in Section 1, subsection “Other Related Work”