  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 O(1)-approximation and prove that no
\PTAS is possible.
