1 Introduction Given a set S of n points in IRd, the Voronoi diagram is a partition of space into cells, such that each cell consists of all points closer to a particular point of S than to any other. Voronoi diagrams are fundamental geometric objects and have a rich literature. They have numerous applications in areas such as pattern recognition and classification, machine learning, robotics, and graphics. Many of these applications are in high dimensions but, unfortunately, the complexity of Voronoi diagrams can be as high as ndd=2e in d dimensions. This has led researchers to investigate the problem of constructing subdivisions that approximate the Voronoi diagram
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