*Result*: A Global Optimization Algorithm for <italic>K</italic>-Center Clustering of One Billion Samples.

*This paper presents a practical global optimization algorithm for the <italic>K</italic>-center clustering problem, which aims to select <italic>K</italic> samples as the cluster centers to minimize the maximum within-cluster distance. Specifically, we propose a reduced-space branch and bound scheme that guarantees convergence to the global optimum in a finite number of steps by only branching on the regions of centers. To improve efficiency, we design a two-stage decomposable lower bound, the solution of which can be derived in a closed form. In addition, we also propose several structure-exploiting acceleration techniques to narrow down the region of centers, including bounds tightening, sample reduction, and parallelization. Extensive studies on synthetic and real-world data sets have demonstrated that our algorithm can solve the <italic>K</italic>-center problems to global optimal within four hours for 10 million samples in the serial mode and 1 billion samples in the parallel mode, whereas existing studies can only address small-scale problems (e.g., thousands of samples). Moreover, compared with the state-of-the-art heuristic methods, the global optimum obtained by our algorithm reduces the objective function by an average of 25.8% on these synthetic and real-world data sets.<italic>This paper was accepted by Chung Piaw Teo, optimization.</italic><bold>Funding:</bold> This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2019-05499].<bold>Supplemental Material:</bold> The data files are available at https://doi.org/10.1287/mnsc.2023.00218. [ABSTRACT FROM AUTHOR]

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