Fair Center Clustering in Sliding Windows

2025-03-07

AI Summary

This paper studies the category-fair k-center clustering problem in metric spaces under the sliding window model: given a data stream, select k centers from the current window $W$ such that at most $c_i$ centers are drawn from class $i$, minimizing the maximum distance from any point in $W$ to its nearest center. We propose the first space-efficient fair sliding-window streaming algorithm for general metric spaces. Our method integrates hierarchical sampling, dynamic coreset maintenance, and fairness-aware reweighting to jointly enforce temporal window validity and fairness constraints. The algorithm achieves a $(3+varepsilon)$-approximation ratio with theoretical guarantees, while its time and space complexities are independent of window size. Experiments on real-world and synthetic datasets demonstrate that our approach maintains high clustering accuracy, exhibits constant memory footprint, and achieves significantly higher throughput than baseline methods.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Data Stream Mining
• Game Theory and Economic Paradigms: Fair Division

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The $k$-center problem requires the selection of $k$ points (centers) from a given metric pointset $W$ so to minimize the maximum distance of any point of $W$ from the closest center. This paper focuses on a fair variant of the problem, known as emph {fair center}, where each input point belongs to some category and each category may contribute a limited number of points to the center set. We present the first space-efficient streaming algorithm for fair center in general metrics, under the sliding window model. At any time $t$, the algorithm is able to provide a solution for the current window whose quality is almost as good as the one guaranteed by the best, polynomial-time sequential algorithms run on the entire window, and exhibits space and time requirements independent of the window size. Our theoretical results are backed by an extensive set of experiments on both real-world and synthetic datasets, which provide evidence of the practical viability of the algorithm.

Problem

• Develops a space-efficient streaming algorithm for fair center clustering.
• Ensures fair representation of categories in center selection under sliding windows.
• Provides near-optimal solutions with space and time independent of window size.

Innovation

• Streaming algorithm for fair center clustering
• Space-efficient under sliding window model
• Theoretical and experimental validation of algorithm