Abstract
Hard-capacitated k-means (HCKM) is one of the fundamental problems remaining open in combinatorial optimization and engineering. In HCKM, one is required to partition a given n-point set into k disjoint clusters with known capacity so as to minimize the sum of within-cluster variances. It is known to be at least APX-hard, and most of the work on it has been done from a meta heuristic or bi-criteria approximation perspective. To the best our knowledge, no constant approximation algorithm or existence proof of such an algorithm is known. As our main contribution, we propose an FPT(k) approximation algorithm with constant performance guarantee for HCKM in this paper.
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Acknowledgements
The first author is supported by Natural Science Foundation of China (No. 11901558) and China Postdoctoral Science Foundation funded project (No. 2018M643233). The second author is supported by the Science Foundation of the Anhui Education Department (No. KJ2019A0834). The third author is supported by Natural Science Foundation of China (No. 11871081). The fourth author is supported by Shenzhen research grant (Nos. KQJSCX20180330170311901, JCYJ20180 305180840138, GGFW2017073114031767).
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Xu, Y., Möhring, R.H., Xu, D. et al. A constant FPT approximation algorithm for hard-capacitated k-means. Optim Eng 21, 709–722 (2020). https://doi.org/10.1007/s11081-020-09503-0
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DOI: https://doi.org/10.1007/s11081-020-09503-0