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The On-Line Heilbronn’s Triangle Problem in Three and Four Dimensions

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Computing and Combinatorics (COCOON 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2387))

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Abstract

In this paper we show lower bounds for the on-line version of Heilbronn’s triangle problem in three and four dimensions. Specifically, we provide incremental constructions for positioning n points in the 3-dimensional (resp., 4-dimensional) unit cube, for which every tetrahedron (resp., pentahedron) defined by four (resp., five) of these points has volume Ω \( \left( {\tfrac{1} {{n^{3.333...} }}} \right) \) (resp., Ω \( \left( {\tfrac{1} {{n^{5.292...} }}} \right) \) ).

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References

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Author information

Authors and Affiliations

  1. The Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Gill Barequet

Authors
  1. Gill Barequet
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, California, 93106, USA

    Oscar H. Ibarra

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore, 117543

    Louxin Zhang

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© 2002 Springer-Verlag Berlin Heidelberg

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Barequet, G. (2002). The On-Line Heilbronn’s Triangle Problem in Three and Four Dimensions. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_39

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  • DOI: https://doi.org/10.1007/3-540-45655-4_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43996-7

  • Online ISBN: 978-3-540-45655-1

  • eBook Packages: Springer Book Archive

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