Improving the first selection lemma in R3

  • Authors:

  • Abdul Basit;Nabil H. Mustafa;Saurabh Ray;Sarfraz Raza

  • Affiliations:

  • LUMS, Lahore, Pakistan;LUMS, Lahore, Pakistan;EPFL, Lausanne, Switzerland;LUMS, Lahore, Pakistan

  • Venue:
  • Proceedings of the twenty-sixth annual symposium on Computational geometry
  • Year:
  • 2010

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Abstract

We present new bounds on the first selection lemma in ℜ3. This makes progress on the open problems of Bukh, Matouaek and Nivash [6] and Boros-Füredi [4] for the three-dimensional case, improving the previously best result of Wagner [8]. While our results narrow the gap between the current best lower and upper bounds, they do not settle this question. However, they indicate that it is the current lower-bounds that are not tight, and we conjecture that the lower-bounds can be further improved to match the current upper bound.