# Fair Clustering for Data Summarization: Improved Approximation Algorithms and Complexity Insights

arXiv: https://arxiv.org/abs/2410.12913 · HTML: https://mlsanity.com/paper/2410.12913/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [Fair k-Center Clustering for Data Summarization](https://mlsanity.com/paper/1901.08628/) (2019)
- [A Survey on Intersectional Fairness in Machine Learning: Notions, Mitigation, and Challenges](https://mlsanity.com/paper/2305.06969/) (2023)
- [Diversity-aware k-median : Clustering with fair center representation](https://mlsanity.com/paper/2106.11696/) (2021)
- [Matroid and Knapsack Center Problems](https://mlsanity.com/paper/1301.0745/) (2013)
- [Approximation Algorithms for Fair Range Clustering](https://mlsanity.com/paper/2306.06778/) (2023)
- [Clustering with fair-center representation: parameterized approximation algorithms and heuristics](https://mlsanity.com/paper/2112.07030/) (2021)
- [Parameterized Approximation Schemes for Clustering with General Norm Objectives](https://mlsanity.com/paper/2304.03146/) (2023)
- [Tight FPT Approximation for Constrained k-Center and k-Supplier](https://mlsanity.com/paper/2110.14242/) (2021)
- [Fair Column Subset Selection](https://mlsanity.com/paper/2306.04489/) (2023)
- [Diversity-aware clustering: Computational Complexity and Approximation Algorithms](https://mlsanity.com/paper/2401.05502/) (2024)
- [Parameterized Approximation for Robust Clustering in Discrete Geometric Spaces](https://mlsanity.com/paper/2305.07316/) (2023)

## Built on by (most cited first, 2 of 2)

- [On the Hardness of Approximation of the Fair k-Center Problem](https://mlsanity.com/paper/2602.16688/) (2026)
- [Parameterized and Streaming Algorithms for Euclidean Fair k-Center Clustering](https://mlsanity.com/paper/2609.06384/) (2026)

## Abstract (arXiv)

Data summarization tasks are often modeled as k-clustering problems, where the goal is to choose k data points, called cluster centers, that best represent the dataset by minimizing a clustering objective. A popular objective is to minimize the maximum distance between any data point and its nearest center, which is formalized as the k-center problem. While in some applications all data points can be chosen as centers, in the general setting, centers must be chosen from a predefined subset of points, referred as facilities or suppliers; this is known as the k-supplier problem. In this work, we focus on fair data summarization modeled as the fair k-supplier problem, where data consists of several groups, and a minimum number of centers must be selected from each group while minimizing the k-supplier objective. The groups can be disjoint or overlapping, leading to two distinct problem variants each with different computational complexity. We present 3-approximation algorithms for both variants, improving the previously known factor of 5. For disjoint groups, our algorithm runs in polynomial time, while for overlapping groups, we present a fixed-parameter tractable algorithm, where the exponential runtime depends only on the number of groups and centers. We show that these approximation factors match the theoretical lower bounds, assuming standard complexity theory conjectures. Finally, using an open-source implementation, we demonstrate the scalability of our algorithms on large synthetic datasets and assess the price of fairness on real-world data, comparing solution quality with and without fairness constraints.