Geometric Packing under Non-uniform Constraints
Computational Geometry
2011-12-01 v2
Abstract
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.
Cite
@article{arxiv.1107.2949,
title = {Geometric Packing under Non-uniform Constraints},
author = {Alina Ene and Sariel Har-Peled and Benjamin Raichel},
journal= {arXiv preprint arXiv:1107.2949},
year = {2011}
}