# Sample-and-Search: An Effective Algorithm for Learning-Augmented k-Median Clustering in High dimensions

arXiv: https://arxiv.org/abs/2603.10721 · HTML: https://mlsanity.com/paper/2603.10721/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 19 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 3 of 3)

- [Faster Matchings via Learned Duals](https://mlsanity.com/paper/2107.09770/) (2021)
- [Near-Linear Time Approximation Schemes for Clustering in Doubling Metrics](https://mlsanity.com/paper/1812.08664/) (2018)
- [Improved Learning-augmented Algorithms for k-means and k-medians Clustering](https://mlsanity.com/paper/2210.17028/) (2022)

## Abstract (arXiv)

In this paper, we investigate the learning-augmented k-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate α ∈ [0,1). This preprocessing step assigns potential labels to the points before clustering. We introduce an algorithm for this problem based on a simple yet effective sampling method, which substantially improves upon the time complexities of existing algorithms. Moreover, we mitigate their exponential dependency on the dimensionality of the Euclidean space. Lastly, we conduct experiments to compare our method with several state-of-the-art learning-augmented k-median clustering methods. The experimental results suggest that our proposed approach can significantly reduce the computational complexity in practice, while achieving a lower clustering cost.