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

摘要

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~((d+1)ln(d-2)+2)).