A fixed-parameter tractable approximation for capacitated k-supplier - Liu, Shuilian; Chen, Xianrun; Xu, Yicheng (Theoretical computer science, 2026)
•We study the uniform-capacitatedk-supplier problem with distinct facility and client sets.•The objective is to minimize the maximum distance between any client and its assigned facility under capacity and cardinality constraints.•We propose the first randomized FPT algorithm for this problem, achieving a 5-approximation.•Our result opens a new algorithmic direction by addressing the problem from a parameterized perspective. Capacitated clustering is a fundamental problem in combinatorial optimization with applications in network design and facility location. While most existing results, such as k-center and sum of radii problems, assume that clients and facilities are co-located, real-world scenarios often involve distinct sets of clients and facility locations. To bridge this discrepancy, we study the uniform-capacitated k-supplier problem, where the facility set and client set are separate. The objective is to minimize the maximum distance between any client and its assigned facility, subject to opening at most k facilities, each of which can serve up to U clients, where U is a uniform capacity bound. The best known result is an 11-approximation algorithm for the non-uniform version in polynomial time. We focus on the uniform case and present the first randomized FPT (fixed-parameter tractable) algorithm achieving a 5-approximation, with running time exponential in k.