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On Center Regions and Balls Containing Many Points

  • Shakhar Smorodinsky
  • Marek Sulovský
  • Uli Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

Abstract

We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in Open image in new window , there is a subset A ⊆ S of size \(\lfloor \frac{d+3}{2}\rfloor\) such that any ball containing A contains at least roughly \(\frac{4}{5ed^3}n\) points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.

Keywords

Convex Body Moment Curve Convex Position Halfspace Depth Containment Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Shakhar Smorodinsky
    • 1
  • Marek Sulovský
    • 2
  • Uli Wagner
    • 2
  1. 1.Department of MathematicsBen-Gurion UniversityBe’er ShevaIsrael
  2. 2.Institute of Theoretical Computer ScienceETH ZurichZurichSwitzerland

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