Dynamic optimality of SplayTTs

Establish that Splay trees on trees (SplayTTs) are dynamically optimal, meaning that they are constant-factor competitive with every optimal dynamic search tree on a tree for an online sequence of queries, analogous to the dynamic-optimality conjecture for classical splay trees.

Background

SplayTTs are presented as a generalization of classical splay trees to search trees on trees. The cited work establishes static optimality: SplayTTs are constant-factor competitive with an optimal static search tree on a tree for an online query sequence. The unresolved stronger claim is dynamic optimality, which would provide constant-factor competitiveness against the best dynamic search tree that may change structure in response to the query sequence, without prior knowledge of that sequence. The paper notes that this would parallel the longstanding dynamic-optimality conjecture for ordinary splay trees in the binary-search-tree setting.