Splay Trees, DavenportSchinzel Sequences, and the Deque Conjecture
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 DavenportSchinzel 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(n alpha^*(n)) time, where alpha^*(n) is the minimum number of applications of the inverseAckermann 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2007
 arXiv:
 arXiv:0707.2160
 Bibcode:
 2007arXiv0707.2160P
 Keywords:

 Computer Science  Data Structures and Algorithms