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Geometric Packing under Non-uniform Constraints

Alina Ene, Benjamin Raichel, and Sariel Har-Peled.

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