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We study the problem of discrete geometric packing. Here, given weighted regions(say in the plane) and points(with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity. We provide a general framework and an algorithm for approximating the optimal solution for packing in hypergraphs arising out of such geometric settings. Using this framework we get a flotilla of results on this problem(and also on its dual, where one wants to pick a maximum weight subset of the points when the regions have capacities). For example, for the case of fat triangles of similar size, we show an

Postscript, PDF.

Submitted to SICOMP November 2012.

Last modified: Mon Nov 26 16:44:50 CST 2012