Geometric packing under nonuniform constraints

Alina Ene, Sariel Har-Peled, Benjamin Raichel

Research output: Contribution to journalArticlepeer-review


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 otilla 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)
Pages (from-to)1745-1784
Number of pages40
JournalSIAM Journal on Computing
Issue number6
StatePublished - 2017


  • Independent set
  • Optimization
  • Rounding scheme

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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