Academic Journal
A Global Optimization Algorithm for K -Center Clustering of One Billion Samples.
| 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.) | |
| Database: | Complementary Index |
| FullText | Text: Availability: 0 CustomLinks: – Url: http://www.jstor.org/openurl?issn=00251909&date=2026&volume=72&issue=6&spage=5106 Name: JSTOR (all content) (s7799221) Category: fullText Text: Icon: https://imageserver.ebscohost.com/branding/jstor/iconJSTOR.gif MouseOverText: Full Text from JSTOR |
|---|---|
| Header | DbId: edb DbLabel: Complementary Index An: 194300943 RelevancyScore: 1162 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1162.4189453125 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: A Global Optimization Algorithm for K -Center Clustering of One Billion Samples. – Name: Author Label: Authors Group: Au 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> – Name: TitleSource Label: Source Group: Src Data: Management Science (INFORMS); Jun2026, Vol. 72 Issue 6, p5106-5130, 25p – Name: Subject Label: Subject Terms Group: Su 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edb&AN=194300943 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1287/mnsc.2023.00218 Languages: – Code: eng Text: English PhysicalDescription: 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. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ren, Jiayang – PersonEntity: Name: NameFull: You, Ningning – PersonEntity: Name: NameFull: Hua, Kaixun – PersonEntity: Name: NameFull: Ji, Chaojie – PersonEntity: Name: NameFull: Cao, Yankai IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00251909 Numbering: – Type: volume Value: 72 – Type: issue Value: 6 Titles: – TitleFull: Management Science (INFORMS) Type: main |
| ResultId | 1 |