## Splay trees, Davenport-Schinzel sequences, and the deque conjecture (2007)

Citations: | 15 - 5 self |

### BibTeX

@MISC{Pettie07splaytrees,,

author = {Seth Pettie},

title = {Splay trees, Davenport-Schinzel sequences, and the deque conjecture },

year = {2007}

}

### OpenURL

### Abstract

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 S, none of whose subsequences are isomorphic to fixed forbidden subsequence. We direct this technique towards Tarjan’s deque conjecture and prove that n deque operations require O(nα ∗ (n)) time, where α ∗ (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.