A constant FPT approximation algorithm for hard-capacitated k-means

01/15/2019

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by   Yicheng Xu, et al.

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Hard-capacitated k-means (HCKM) is one of the fundamental problems remaining open in combinatorial optimization and data mining areas. In this problem, 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 for which most of the work is from a meta heuristic 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) algorithm with performance guarantee of 69+ϵ for any HCKM instances in this paper.