A Global Optimization Algorithm for K-Center Clustering of One Billion Samples
Abstract
This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a reduced-space branch and bound scheme and guarantees convergence to the global optimum in a finite number of steps by only branching on the regions of centers. To improve efficiency, we have designed a two-stage decomposable lower bound, the solution of which can be derived in a closed form. In addition, we also propose several acceleration techniques to narrow down the region of centers, including bounds tightening, sample reduction, and parallelization. Extensive studies on synthetic and real-world datasets have demonstrated that our algorithm can solve the K-center problems to global optimal within 4 hours for ten million samples in the serial mode and one billion samples in the parallel mode. Moreover, compared with the state-of-the-art heuristic methods, the global optimum obtained by our algorithm can averagely reduce the objective function by 25.8% on all the synthetic and real-world datasets.
Cite
@article{arxiv.2301.00061,
title = {A Global Optimization Algorithm for K-Center Clustering of One Billion Samples},
author = {Jiayang Ren and Ningning You and Kaixun Hua and Chaojie Ji and Yankai Cao},
journal= {arXiv preprint arXiv:2301.00061},
year = {2026}
}
Comments
34 pages, 6 figures, and 5 tables. This paper is accepted by Managment Science. The final published version of this article is available at: https://pubsonline.informs.org/doi/10.1287/mnsc.2023.00218