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The On-Line Heilbronn's Triangle Problem in d Dimensions

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Abstract

In this paper we show a lower bound for the on-line version of Heilbronn's triangle problem in d dimensions. Specifically, we provide an incremental construction for positioning n points in the d-dimensional unit cube, for which every simplex defined by d + 1 of these points has volume Ω(1/n(d+1)ln(d-2)-0.265 d+2.269) (for d ≥ 5).

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Correspondence to Gill Barequet or Alina Shaikhet.

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Barequet, G., Shaikhet, A. The On-Line Heilbronn's Triangle Problem in d Dimensions. Discrete Comput Geom 38, 51–60 (2007). https://doi.org/10.1007/s00454-007-1323-x

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Keywords

  • Discrete Comput Geom
  • Spherical Packing
  • Dimensional Sphere
  • Small Triangle
  • Incremental Construction