Approximation Schemes for Capacitated Clustering in Doubling Metrics
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Motivated by applications in redistricting, we consider the uniform capacitated k-median and uniform capacitated k-means problems in bounded doubling metrics. We provide the first QPTAS for both problems and the first PTAS for the uniform capacitated k-median problem for points in R^2 . This is the first improvement over the bicriteria QPTAS for capacitated k-median in low-dimensional Euclidean space of Arora, Raghavan, Rao [STOC 1998] (1 + ϵ-approximation, 1 + ϵ-capacity violation) and arguably the first polynomial-time approximation algorithm for a non-trivial metric.
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