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Transversals and Epsilon Nets

  • Jiří Matoušek
Part of the Graduate Texts in Mathematics book series (GTM, volume 212)

Abstract

Here we are going to consider problems of the following type: We have a family F of geometric shapes satisfying certain conditions, and we would like to conclude that F can be “pierced” by not too many points, meaning that we can choose a bounded number of points such that each set of F contains at least one of them. Such questions are sometimes called Gallai-type problems, because of the following nice problem raised by Gallai: Let F be a finite family of closed disks in the plane such that every two disks in F intersect. What is the smallest number of points needed to pierce F For this problem, the exact answer is known: 4 points always suffice and are sometimes necessary.

Keywords

Fractional Packing Finite Family Line Transversal Common Tangent Helly Number 
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 New York, Inc. 2002

Authors and Affiliations

  • Jiří Matoušek
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic

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