Splay trees, Davenport-Schinzel sequences, and the deque conjecture

We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a Davenport-Schinzel sequence, none of whose subsequences are isomorphic to a fixed forbidden subsequence. We direct this technique towards Tarjan's deque conjecture and prove that n deque operations take only O(n (n)) time, where (n) is the minimum number of applications of the inverse-Ackermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures.

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Seth Pettie
• Keywords: Algorithms, Asymptotic Performance, SODA 2008, Splay Trees, Tarjan's Deque Conjecture