# Heuristic Approaches to Obtain Low-Discrepancy Point Sets via Subset Selection

arXiv: https://arxiv.org/abs/2306.15276 · HTML: https://mlsanity.com/paper/2306.15276/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2023.

## Built on by (most cited first, 5 of 5)

- [Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks](https://mlsanity.com/paper/2405.15059/) (2024)
- [carps: A Framework for Comparing N Hyperparameter Optimizers on M Benchmarks](https://mlsanity.com/paper/2506.06143/) (2025)
- [Optimizing Kernel Discrepancies via Subset Selection](https://mlsanity.com/paper/2511.02706/) (2025)
- [Quasi-Random Physics-informed Neural Networks](https://mlsanity.com/paper/2507.08121/) (2025)
- [A Bayesian Approach to Low-Discrepancy Subset Selection](https://mlsanity.com/paper/2602.14607/) (2026)

## Abstract (arXiv)

Building upon the exact methods presented in our earlier work [J. Complexity, 2022], we introduce a heuristic approach for the star discrepancy subset selection problem. The heuristic gradually improves the current-best subset by replacing one of its elements at a time. While we prove that the heuristic does not necessarily return an optimal solution, we obtain very promising results for all tested dimensions. For example, for moderate point set sizes 30 ≤ n ≤ 240 in dimension 6, we obtain point sets with L∞ star discrepancy up to 35% better than that of the first n points of the Sobol' sequence. Our heuristic works in all dimensions, the main limitation being the precision of the discrepancy calculation algorithms. We also provide a comparison with a recent energy functional introduced by Steinerberger [J. Complexity, 2019], showing that our heuristic performs better on all tested instances.