Geometric Packing under Non-uniform Constraints

Alina Ene; Sariel Har-Peled; Benjamin Raichel

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arXiv · 1107.2949

Geometric Packing under Non-uniform Constraints

Alina Ene·Sariel Har-Peled·Benjamin Raichel

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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.

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Alina Ene, Sariel Har-Peled, Benjamin Raichel. 2011-11-29. Geometric Packing under Non-uniform Constraints. https://arxiv.org/abs/1107.2949

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