We study the min-max Voronoi diagram of a set S of polygonal objects, a generalization of Voronoi diagrams based on the maximum distance between a point and a polygon. We show that the min-max Voronoi diagram is equivalent to the Voronoi diagram under the Hausdorff distance function. We investigate the combinatorial properties of this diagram and give improved combinatorial bounds and algorithms. As a byproduct we introduce the min-max hull which relates to the min-max Voronoi diagram in the way a convex hull relates to the ordinary Voronoi diagram.
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