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Pankaj K. Agarwal : Union of geometric objects, epsilon-nets, and hitting sets

The combinatorial complexity of the union of a set of geometric objects is the total number of faces of all dimensions that lie on the boundary of the union. We review some recent results on the complexity of the union of geometric objects in 2d and 3D satisfying various natural conditions and on computing the union. We then discuss the critical roles they play in computing an epsilon net and a hitting set of a set system.

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