Abstract

We show that multi-splay trees have most of the properties that splay trees have. Specifically, we show that multi-splay trees have the following properties: the access lemma, static optimality, the static finger property, the working set property, and key-independent optimality. Moreover, we prove that multi-splay trees have the deque property, which was conjectured by Tarjan in 1985 for splay trees, but remains unproven despite a significant amount of research toward proving it. Efficiently maintaining and manipulating sets of elements from a totally ordered universe is a fundamental problem in computer science. Specifically, many algorithms need a data structure that can efficiently support at least the following operations: insert, delete, predecessor, and successor, as well as membership testing. A standard data structure that maintains a totally ordered set and

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