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 \(^{\rm ({\it d}+1)ln ({\it d}--2)+2}\)).
Work on this paper by the first author has been supported in part by the European FP6 Network of Excellence Grant 506766 (AIM@SHAPE).
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References
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Barequet, G., Shaikhet, A. (2006). The On-Line Heilbronn’s Triangle Problem in d Dimensions. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_43
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DOI: https://doi.org/10.1007/11809678_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36925-7
Online ISBN: 978-3-540-36926-4
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