Epsilon-Nets for Halfspaces Revisited

Sariel Har-Peled, Haim Kaplan, Micha Sharir, Shakhar Smorodinsky

Research output: Working paper/PreprintPreprint


Given a set P of n points in R 3 , we show that, for any ε > 0, there exists an ε-net of P for halfspace ranges, of size O(1/ε). We give five proofs of this result, which are arguably simpler than previous proofs [MSW90, CV07, PR08]. We also consider several related variants of this result, including the case of points and pseudo-disks in the plane.
Original languageEnglish GB
PublisherarXiv:1410.3154 [cs.CG]
StatePublished - 12 Oct 2014


  • Computer Science - Computational Geometry


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