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

In this paper we consider the k-clustering problem for a set S of n points pi = (~i) in the d-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 of intracluster errors over every cluster is used, and as the int racluster criterion of a cluster Sj,