A constant parameterized approximation for hard-capacitated k-means
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Hard-capacitated k-means (HCKM) is one of the remaining fundamental problems for which if there exist polynomial time constant factor approximation is not clear. But what we know is that it is at least APX-hard. Most of the existing as well as the state-of-the-art constant-factor results for hard-capacitated min-sum k-clusterings are pseudo-approximations that violate either the capacity or the cardinality constraints. In this paper, we propose an FPT approximation for HCKM without violating any hard constraints whose running time is 2^O(k k)n^O(1) and performance guarantee is 69+ϵ.
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