We study learning-augmented binary search trees (BSTs) and B-Trees via Treaps with composite priorities. The result is a simple search tree where the depth of each item is determined by its predicted weight $w_x$. To achieve the result, each item $x$ has its composite priority $-\lfloor\log\log(1/w_x)\rfloor + U(0, 1)$ where $U(0, 1)$ is the uniform random variable. This generalizes the recent learning-augmented BSTs [Lin-Luo-Woodruff ICML`22], which only work for Zipfian distributions, to arbitrary inputs and predictions. It also gives the first B-Tree data structure that can provably take advantage of localities in the access sequence via online self-reorganization. The data structure is robust to prediction errors and handles insertions, deletions, as well as prediction updates.

翻译：我们通过具有复合优先级的Treap结构研究了学习增强型二叉搜索树（BST）与B树。其成果是一种简单搜索树，其中每个节点的深度由其预测权重$w_x$决定。为实现该结果，每个节点$x$的复合优先级定义为$-\lfloor\log\log(1/w_x)\rfloor + U(0, 1)$，其中$U(0, 1)$为均匀随机变量。该工作将近期仅适用于Zipf分布的学习增强型BST [Lin-Luo-Woodruff ICML`22] 推广至任意输入与预测场景，同时首次提出了能够通过在线自重组机制在访问序列中利用局部性的B树数据结构。该数据结构对预测误差具有鲁棒性，并支持插入、删除操作以及预测更新。