Selection Lemmas for Various Geometric Objects

  title={Selection Lemmas for Various Geometric Objects},
  author={P. Ashok and Sathish Govindarajan and Ninad Rajgopal},
Selection lemmas are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection lemma type results typically show that there exists a point that is contained in many objects that are induced (spanned) by an underlying point set. In the first selection lemma, we consider the set of all the objects induced by a point set P. This question has been widely explored for… Expand
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This work proves an exact result on the strong and the weak variant of the First Selection Lemma for rectangles and shows exact combinatorial bounds on the hitting set problem for two special classes of induced axis-parallel rectangles. Expand
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Improved bounds on the first selection lemma in ℝ3 are presented and it is proved that c3≤1/44≈0.00227, improving the previous best result of c3=0.000227 and making progress, for the three-dimensional case, on the open problems. Expand
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Lectures on discrete geometry
  • J. Matousek
  • Computer Science, Mathematics
  • Graduate texts in mathematics
  • 2002
This book is primarily a textbook introduction to various areas of discrete geometry, in which several key results and methods are explained, in an accessible and concrete manner, in each area. Expand
A Point in Many Triangles
  • B. Bukh
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 2006
We give a simpler proof of the result of Boros and Furedi that for any finite set of points in the plane in general position there is a point lying in $2/9$ of all the triangles determined by theseExpand
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Selecting Heavily Covered Points
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