Balanced k-Center Clustering When k Is A Constant

The problem of constrained k-center clustering has attracted significant attention in the past decades. In this paper, we study balanced k-center cluster where the size of each cluster is constrained by the given lower and upper bounds. The problem is motivated by the applications in processing and analyzing large-scale data in high dimension. We provide a simple nearly linear time 4-approximation algorithm when the number of clusters k is assumed to be a constant. Comparing with existing method, our algorithm improves the approximation ratio and significantly reduces the time complexity. Moreover, our result can be easily extended to any metric space.