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The bi-criteria seeding algorithms for two variants of k-means problem

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  • Min Li

    (Shandong Normal University)

Abstract

The k-means problem is very classic and important in computer science and machine learning, so there are many variants presented depending on different backgrounds, such as the k-means problem with penalties, the spherical k-means clustering, and so on. Since the k-means problem is NP-hard, the research of its approximation algorithm is very hot. In this paper, we apply a bi-criteria seeding algorithm to both k-means problem with penalties and spherical k-means problem, and improve (upon) the performance guarantees given by the k-means++ algorithm for these two problems.

Suggested Citation

  • Min Li, 2022. "The bi-criteria seeding algorithms for two variants of k-means problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1693-1704, October.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00537-9
    DOI: 10.1007/s10878-020-00537-9
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    References listed on IDEAS

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    1. Dongmei Zhang & Dachuan Xu & Yishui Wang & Peng Zhang & Zhenning Zhang, 2018. "A local search approximation algorithm for a squared metric k-facility location problem," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1168-1184, May.
    2. Lu Han & Dachuan Xu & Donglei Du & Dongmei Zhang, 2018. "A local search approximation algorithm for the uniform capacitated k-facility location problem," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 409-423, February.
    3. Min Li & Dachuan Xu & Jun Yue & Dongmei Zhang & Peng Zhang, 2020. "The seeding algorithm for k-means problem with penalties," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 15-32, January.
    4. Min Li & Dachuan Xu & Jun Yue & Dongmei Zhang, 2020. "The Parallel Seeding Algorithm for k-Means Problem with Penalties," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-18, August.
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