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The combinatorial complexities of (1) the Voronoi diagram of moving points in 2D and (2) the Voronoi diagram of lines in 3D, both under the Euclidean metric, continues to challenge geometers because of the open gap between the (n 2) lower bound and the O(n 3+ε) upper bound. Each of these two combinatorial problems has a closely related problem involving(More)
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