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• W3105232823 abstract "We show that the union of n translates of a convex body in $$mathbb {R}^3$$ can have $$varTheta (n^3)$$ holes in the worst case, where a hole in a set X is a connected component of $$mathbb {R}^3 setminus X$$ . This refutes a 20-year-old conjecture. As a consequence, we also obtain improved lower bounds on the complexity of motion planning problems and of Voronoi diagrams with convex distance functions." @default.
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• W3105232823 date "2016-09-16" @default.
• W3105232823 modified "2023-09-25" @default.
• W3105232823 title "The Number of Holes in the Union of Translates of a Convex Set in Three Dimensions" @default.
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• W3105232823 doi "https://doi.org/10.1007/s00454-016-9820-4" @default.
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