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Point Selections and Weak ε-Nets for Convex Hulls

  • Noga Alon (a1), Imre Bárány (a2), Zoltán Füredi (a3) and Daniel J. Kleitman (a4)

One of our results: let X be a finite set on the plane, 0 < ε < 1, then there exists a set F (a weak ε-net) of size at most 7/ε2 such that every convex set containing at least ε|X| elements of X intersects F. Note that the size of F is independent of the size of X.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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