# On the Power of Learning-Augmented Search Trees

arXiv: https://arxiv.org/abs/2211.09251 · HTML: https://mlsanity.com/paper/2211.09251/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 61 references that are in the map.
- First posted on arXiv 16 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [The Case for Learned Index Structures](https://mlsanity.com/paper/1712.01208/) (2017)
- [Algorithms with Predictions](https://mlsanity.com/paper/2006.09123/) (2020)
- [A Survey on Session-based Recommender Systems](https://mlsanity.com/paper/1902.04864/) (2019)
- [Faster Matchings via Learned Duals](https://mlsanity.com/paper/2107.09770/) (2021)
- [Faster Fundamental Graph Algorithms via Learned Predictions](https://mlsanity.com/paper/2204.12055/) (2022)
- [Learning Augmented Binary Search Trees](https://mlsanity.com/paper/2206.12110/) (2022)
- [Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing](https://mlsanity.com/paper/2011.11743/) (2020)
- [Learning-Augmented k-means Clustering](https://mlsanity.com/paper/2110.14094/) (2021)
- [Online Graph Algorithms with Predictions](https://mlsanity.com/paper/2112.11831/) (2021)
- [Triangle and Four Cycle Counting with Predictions in Graph Streams](https://mlsanity.com/paper/2203.09572/) (2022)
- [Updatable Learned Index with Precise Positions](https://mlsanity.com/paper/2104.05520/) (2021)
- [(Optimal) Online Bipartite Matching with Degree Information](https://mlsanity.com/paper/2110.11439/) (2021)
- [Learning-Augmented Maximum Flow](https://mlsanity.com/paper/2207.12911/) (2022)
- [Learning-Augmented Query Policies for Minimum Spanning Tree with Uncertainty](https://mlsanity.com/paper/2206.15201/) (2022)
- [Competitive Online Search Trees on Trees](https://mlsanity.com/paper/1908.00848/) (2019)
- [In pursuit of the dynamic optimality conjecture](https://mlsanity.com/paper/1306.0207/) (2013)
- [Pinning Down the Strong Wilber 1 Bound for Binary Search Trees](https://mlsanity.com/paper/1912.02900/) (2019)

## Built on by (most cited first, 3 of 3)

- [Robust Learning-Augmented Dictionaries](https://mlsanity.com/paper/2402.09687/) (2024)
- [The Predicted-Updates Dynamic Model: Offline, Incremental, and Decremental to Fully Dynamic Transformations](https://mlsanity.com/paper/2307.08890/) (2023)
- [Privacy-Preserving Learning-Augmented Data Structures](https://mlsanity.com/paper/2510.00165/) (2025)

## Abstract (arXiv)

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 wx. Specifically, each item x is assigned a composite priority of -lfloorloglog(1/wx)rfloor + U(0, 1) where U(0, 1) is the uniform random variable. By choosing wx 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.