Geometric packing under non-uniform constraints

Alina Ene, Sariel Har-Peled, Benjamin Raichel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationProceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012
Pages11-20
Number of pages10
DOIs
StatePublished - Jul 23 2012
Event28th Annual Symposuim on Computational Geometry, SCG 2012 - Chapel Hill, NC, United States
Duration: Jun 17 2012Jun 20 2012

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

Other28th Annual Symposuim on Computational Geometry, SCG 2012
CountryUnited States
CityChapel Hill, NC
Period6/17/126/20/12

Keywords

  • Independent set
  • Optimization
  • Rounding scheme

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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