We consider the design of adaptive data structures for searching elements of a tree-structured space. We use a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of vertices of a tree. This model is based on a simple structure for decomposing graphs, previously known under several names including elimination trees, vertex rankings, and tubings. The model is equivalent to the classical binary search tree model exactly when the underlying tree is a path. We describe an online O(log log n)-competitive search tree data structure in this model, where n is the number of vertices. This matches the best-known competitive ratio of binary search trees. Our method is inspired by Tango trees, an online binary search tree algorithm, but critically needs several new notions including one that we call Steiner-closed search trees, which may be of independent interest. Moreover, our technique is based on a novel use of two levels of decomposition, first from search space to a set of Steiner-closed trees and, second, from these trees into paths.

我们考虑设计用于搜索树结构空间元素的自适应数据结构。我们使用基于旋转的在线二叉搜索树模型的自然推广，其中底层搜索空间是树的顶点集。该模型基于用于分解图的简单结构，以前有多个名称，包括消除树、顶点排序和管道。当底层树是路径时，该模型完全相当于经典的二叉搜索树模型。我们在此模型中描述了一个在线O (log log n )-竞争搜索树数据结构，其中n是顶点数。这与二叉搜索树最著名的竞争比相匹配。我们的方法受到 Tango 树（一种在线二叉搜索树算法）的启发，但迫切需要几个新概念，包括我们称为 Steiner 封闭搜索树的概念，它可能具有独立的兴趣。此外，我们的技术基于两级分解的新颖使用，首先从搜索空间到一组斯坦纳闭树，其次从这些树到路径。