Heilbronn's triangle problem

Authors:
Gill Barequet;Alina Shaikhet
Affiliations:
Technion-Israel Inst. of Technology, Haifa, Israel;Technion-Israel Inst. of Technology, Haifa, Israel
Venue:
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Year:
2007

Citing 4
Cited 0

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An Upper Bound for the d-Dimensional Analogue of Heilbronn's Triangle Problem

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The on-line heilbronn’s triangle problem in d dimensions

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Abstract

In the famous Heilbronn's triangle problem, one aims to find a point set S (say, in the plane), in which the smallest area of a triangle defined by three points of S assumes its maximum. In this video segment we present some variants of the problem. We show a few optimal, or almost optimal, configurations of small numbers of points, and generalize the problem to higher dimensions. Then, we make the distinction between the off-line and on-line versions of the problem, and outline an efficient procedure for attacking the latter version of the problem.