A PTAS Framework for Clustering Problems in Doubling Metrics

Constrained clustering problems have been studied extensively in recent years. In this paper, we focus on a class of constrained k-median problems with general constraints on facilities, denoted as GCF k-CMedian problems. We present a randomized polynomial-time approximation scheme (PTAS) framework based on the split-tree decomposition and dynamic programming process for GCF k-CMedian problems, such as k-median with service installation costs, k-facility location and priority k-median problems in doubling metrics.