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.
Submitted to SICOMP November 2012.
Last modified: Mon Nov 26 16:44:50 CST 2012