Applications of weighted Voronoi diagrams and randomization to variance-based k-clustering

In this paper we consider thek-clustering problem for a set S of n points i=(xi) in thed-dimensional space with variance-based errors as clustering criteria, motivated from the color quantization problem of computing a color lookup table for frame buffer display. As the inter-cluster criterion to minimize, the sum on intra-cluster errors over every cluster is used, and as the intra-cluster criterion of a cluster Sj,