Fair Range k-Supplier Clustering in Offline and Streaming Models

Fairness has emerged as a central consideration in machine learning, motivating the study of fair range $k$-supplier clustering as a fundamental problem that focuses fairness on the selected centers. Given a set of suppliers and clients, where each supplier may belong to one or more demographic or functional groups, the objective is to select $k$ suppliers that minimize the maximum client-to-center distance while ensuring that the number of selected suppliers from each group satisfies prescribed lower and upper bounds. For disjoint supplier groups, we develop a polynomial-time $3$-approximation algorithm in the offline setting and a $(3+\epsilon)$-approximation algorithm in the streaming setting. We further consider overlapping supplier groups and show that this generalization admits a parameterized $3$-approximation algorithm whose runtime is exponential in the number of clusters. Finally, experiments on both synthetic and real-world datasets demonstrate that our algorithms achieve significantly better clustering quality and runtime efficiency in comparison with state-of-the-art methods.