Approximation Algorithm for Constrained $k$-Center Clustering: A Local Search Approach

• URL: http://arxiv.org/abs/2601.11883v1
• Date: Sat, 17 Jan 2026 02:39:41 GMT
• Title: Approximation Algorithm for Constrained $k$-Center Clustering: A Local Search Approach
• Authors: Chaoqi Jia, Longkun Guo, Kewen Liao, Zhigang Lu, Chao Chen, Jason Xue,
• Abstract summary: We study the constrained k-center clustering problem, where instance-level cannot-link (CL) and must-link (ML) constraints are incorporated as background knowledge.<n>We propose a novel local search framework based on a transformation to a dominating matching set problem, achieving the best possible approximation ratio of 2.
• Score: 10.257446766550862
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any improvement to a ratio of 2 - ε would imply P = NP. In this work, we study the constrained k-center clustering problem, where instance-level cannot-link (CL) and must-link (ML) constraints are incorporated as background knowledge. Although general CL constraints significantly increase the hardness of approximation, previous work has shown that disjoint CL sets permit constant-factor approximations. However, whether local search can achieve such a guarantee in this setting remains an open question. To this end, we propose a novel local search framework based on a transformation to a dominating matching set problem, achieving the best possible approximation ratio of 2. The experimental results on both real-world and synthetic datasets demonstrate that our algorithm outperforms baselines in solution quality.

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