展树、Davenport-Schinzel序列和Deque猜想
Splay Trees, Davenport-Schinzel Sequences, and the Deque Conjecture
摘要：
我们引入了一种新的技术来限制splay树的渐近性能。其基本思想是以间接的方式将展开树的旋转转化为Davenport-Schinzel序列S，S的连续性都不同构于固定的禁止子序列。我们将这种技术引向Tarjan的双端猜想，并证明了n个双端操作需要O（n alpha^*（n））时间，其中alpha^*（n）是逆Ackermann函数映射n到常数的最小应用次数。我们乐观地认为，这种方法可以直接用于其他开放的分支树，如遍历和分裂分支。
英文摘要：
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(n alpha^*(n)) time, where alpha^*(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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
