Learning-Augmented B-Trees

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 -⌊loglog(1/w_x)⌋ + 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.