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).
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1007/s00454-007-1323-x