GIST: Greedy Independent Set Thresholding for Max-Min Diversification with Submodular Utility
Matthew Fahrbach, Srikumar Ramalingam, Morteza Zadimoghaddam, Sara Ahmadian, Gui Citovsky, Giulia DeSalvo
Abstract
This work studies a novel subset selection problem called *max-min diversification with monotone submodular utility* (MDMS), which has a wide range of applications in machine learning, e.g., data sampling and feature selection. Given a set of points in a metric space, the goal of MDMS is to maximize $f(S) = g(S) + \lambda \cdot \text{div}(S)$ subject to a cardinality constraint $|S| \le k$, where $g(S)$ is a monotone submodular function and $\text{div}(S) = \min_{u,v \in S : u \ne v} \text{dist}(u,v)$ is the *max-min diversity* objective. We propose the `GIST` algorithm, which gives a $\frac{1}{2}$-approximation guarantee for MDMS by approximating a series of maximum independent set problems with a bicriteria greedy algorithm. We also prove that it is NP-hard to approximate within a factor of $0.5584$. Finally, we show in our empirical study that `GIST` outperforms state-of-the-art benchmarks for a single-shot data sampling task on ImageNet.
BibTeX
@inproceedings{
fahrbach2025gist,
title={{GIST}: Greedy Independent Set Thresholding for Max-Min Diversification with Submodular Utility},
author={Matthew Fahrbach and Srikumar Ramalingam and Morteza Zadimoghaddam and Sara Ahmadian and Gui Citovsky and Giulia DeSalvo},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=5aeD5UbiLv}
}