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On parameterized approximation algorithms for balanced clustering

Author

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  • Xiangyan Kong

    (Central South University)

  • Zhen Zhang

    (Hunan University of Technology and Business)

  • Qilong Feng

    (Central South University)

Abstract

Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facility is constrained by the given lower and upper bounds. It was known that both the problems of balanced k-means and k-median are W[2]-hard if parameterized by k, implying that the existences of FPT(k)-time exact algorithms for these problems are unlikely. In this paper, we give FPT(k)-time $$(9+\epsilon )$$ ( 9 + ϵ ) -approximation and $$(3+\epsilon )$$ ( 3 + ϵ ) -approximation algorithms for balanced k-means and k-median respectively, improving upon the previous best approximation ratios of $$86.9+\epsilon $$ 86.9 + ϵ and $$7.2+\epsilon $$ 7.2 + ϵ obtained in the same time. Our main technical contribution and the crucial step in getting the improved ratios is a different random sampling method for selecting opened facilities.

Suggested Citation

  • Xiangyan Kong & Zhen Zhang & Qilong Feng, 2023. "On parameterized approximation algorithms for balanced clustering," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-14, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00980-w
    DOI: 10.1007/s10878-022-00980-w
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    References listed on IDEAS

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    1. Borgwardt, S. & Brieden, A. & Gritzmann, P., 2017. "An LP-based k-means algorithm for balancing weighted point sets," European Journal of Operational Research, Elsevier, vol. 263(2), pages 349-355.
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