Zeyu Lin | Search arXiv

arXiv2026

Parameterized and Streaming Algorithms for Euclidean Fair $k$-Center Clustering

Motivated by the growing importance of fairness in machine learning, fair $k$-center clustering has attracted considerable research attention as a fundamental problem. In this problem, a dataset is partitioned into $m$ disjoint groups, and the objective is to select $k$ data points as centers, subject to upper bounds on the number of centers chosen from each group, aiming to minimize the maximum distance between any data point and its assigned center. Focusing on Euclidean spaces, which are ubiquitous in machine learning applications, we first develop a parameterized approximation algorithm for Euclidean fair $k$-center with an approximation ratio of $2.732$. By incorporating this algorithm as a post-processing stage into a one-pass streaming framework for large-scale data, we obtain an approximation ratio of $4.464$. These ratios can be further respectively improved to $2.414$ and $3.828$ with a runtime exponential on $k$. To ensure polynomial-time complexity, we further design a one-pass streaming algorithm with an approximation ratio of $4.732$, which can be further improved to $4.42$, outperforming the state-of-the-art ratio. Finally, extensive experiments show that our methods significantly outperform state-of-the-art approaches in terms of clustering accuracy.

cs.LG↗

arXiv2025

Improved Streaming Algorithm for Fair $k$-Center Clustering

Many real-world applications pose challenges in incorporating fairness constraints into the $k$-center clustering problem, where the dataset consists of $m$ demographic groups, each with a specified upper bound on the number of centers to ensure fairness. Focusing on big data scenarios, this paper addresses the problem in a streaming setting, where data points arrive one by one sequentially in a continuous stream. Leveraging a structure called the $\lambda$-independent center set, we propose a one-pass streaming algorithm that first computes a reserved set of points during the streaming process. Then, for the post-streaming process, we propose an approach for selecting centers from the reserved point set by analyzing all three possible cases, transforming the most complicated one into a specially constrained vertex cover problem in an auxiliary graph. Our algorithm achieves a tight approximation ratio of 5 while consuming $O(k\log n)$ memory. It can also be readily adapted to solve the offline fair $k$-center problem, achieving a 3-approximation ratio that matches the current state of the art. Furthermore, we extend our approach to a semi-structured data stream, where data points from each group arrive in batches. In this setting, we present a 3-approximation algorithm for $m = 2$ and a 4-approximation algorithm for general $m$. Lastly, we conduct extensive experiments to evaluate the performance of our approaches, demonstrating that they outperform existing baselines in both clustering cost and runtime efficiency.

cs.DS↗