Heilbronn's triangle problem

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Heilbronn's triangle problem

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Annual Symposium on Computational Geometry archive
Proceedings of the twenty-third annual symposium on Computational geometry table of contents

Gyeongju, South Korea

SESSION: Session 4A: video session table of contents

Pages: 127 - 128

Year of Publication: 2007

ISBN:978-1-59593-705-6

Authors

Gill Barequet	Technion-Israel Inst. of Technology, Haifa, Israel
Alina Shaikhet	Technion-Israel Inst. of Technology, Haifa, Israel

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
ACM: Association for Computing Machinery
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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ACM New York, NY, USA

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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.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Gill Barequet, A Lower Bound for Heilbronn's Triangle Problem in d Dimensions, SIAM Journal on Discrete Mathematics, v.14 n.2, p.230-236, 2001 [doi>10.1137/S0895480100365859]
	2	G. Barequet, The on-line Heilbronn's triangle problem, Discrete Mathematics, 283 (2004), 7--14.
	3	G. Barequet and A. Shaikhet, The on-line Heilbronn's triangle problem in d dimensions, Discrete & Computational Geometry, in press. Preliminary version in Proc. 12th COCOON, Taipei, Taiwan, LNCS, 4112, Springer-Verlag, 408--417, August 2006.
	4	Peter Brass, An Upper Bound for the d-Dimensional Analogue of Heilbronn's Triangle Problem, SIAM Journal on Discrete Mathematics, v.19 n.1, p.192-195, 2005 [doi>10.1137/S0895480103435810]
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