On the Power of Learning-Augmented Search Trees

TL;DR

This paper introduces a learning-augmented search tree design that adapts to arbitrary distributions, achieves static optimality, and supports dynamic operations with robustness, outperforming prior methods in empirical evaluations.

Contribution

It extends learning-augmented BSTs to general distributions, incorporates self-reorganization for locality, and generalizes to B-Trees, supporting dynamic updates and robustness.

Findings

Achieves static optimality for arbitrary distributions

Supports dynamic operations like insertions and deletions

Outperforms prior learning-augmented and classic data structures in experiments

Abstract

We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each item $x$ is assigned a composite priority of $-\lfloor\log\log(1/w_x)\rfloor + U(0, 1)$ where $U(0, 1)$ is the uniform random variable. By choosing $w_x$ as the relative frequency of $x$, the resulting search trees achieve static optimality. This approach generalizes the recent learning-augmented BSTs [Lin-Luo-Woodruff ICML '22], which only work for Zipfian distributions, by extending them to arbitrary input distributions. Furthermore, we demonstrate that our method can be generalized to a B-Tree data structure using the B-Treap approach [Golovin ICALP '09]. Our search trees are also capable of leveraging localities in the access sequence through online self-reorganization, thereby achieving the working-set property. Additionally, they are robust to prediction errors and support dynamic operations, such as insertions, deletions, and prediction updates. We complement our analysis with an empirical study, demonstrating that our method outperforms prior work and classic data structures.