Academic Journal

A Global Optimization Algorithm for K -Center Clustering of One Billion Samples.

Bibliographic Details
Title: A Global Optimization Algorithm for K -Center Clustering of One Billion Samples.
Authors: Ren, Jiayang, You, Ningning, Hua, Kaixun, Ji, Chaojie, Cao, Yankai
Source: Management Science (INFORMS); Jun2026, Vol. 72 Issue 6, p5106-5130, 25p
Subject Terms: Branch & bound algorithms, Clustering algorithms, Parallel programming, Global optimization, Centroid, Optimization algorithms, Big data
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. 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 K-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. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2019-05499]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.00218. [ABSTRACT FROM AUTHOR]
Copyright of Management Science (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A Global Optimization Algorithm for K -Center Clustering of One Billion Samples.
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  Data: <searchLink fieldCode="AR" term="%22Ren%2C+Jiayang%22">Ren, Jiayang</searchLink><br /><searchLink fieldCode="AR" term="%22You%2C+Ningning%22">You, Ningning</searchLink><br /><searchLink fieldCode="AR" term="%22Hua%2C+Kaixun%22">Hua, Kaixun</searchLink><br /><searchLink fieldCode="AR" term="%22Ji%2C+Chaojie%22">Ji, Chaojie</searchLink><br /><searchLink fieldCode="AR" term="%22Cao%2C+Yankai%22">Cao, Yankai</searchLink>
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  Data: Management Science (INFORMS); Jun2026, Vol. 72 Issue 6, p5106-5130, 25p
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Branch+%26+bound+algorithms%22">Branch & bound algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Clustering+algorithms%22">Clustering algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel+programming%22">Parallel programming</searchLink><br /><searchLink fieldCode="DE" term="%22Global+optimization%22">Global optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Centroid%22">Centroid</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Big+data%22">Big data</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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. 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 K-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. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2019-05499]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.00218. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Management Science (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1287/mnsc.2023.00218
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 25
        StartPage: 5106
    Subjects:
      – SubjectFull: Branch & bound algorithms
        Type: general
      – SubjectFull: Clustering algorithms
        Type: general
      – SubjectFull: Parallel programming
        Type: general
      – SubjectFull: Global optimization
        Type: general
      – SubjectFull: Centroid
        Type: general
      – SubjectFull: Optimization algorithms
        Type: general
      – SubjectFull: Big data
        Type: general
    Titles:
      – TitleFull: A Global Optimization Algorithm for K -Center Clustering of One Billion Samples.
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            NameFull: Ren, Jiayang
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            NameFull: You, Ningning
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            NameFull: Hua, Kaixun
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            NameFull: Ji, Chaojie
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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