Point sets in the unit square and large areas of convex hulls of subsets of points

Hanno Lefmann ()
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Hanno Lefmann: TU Chemnitz

Journal of Combinatorial Optimization, 2008, vol. 16, issue 2, No 8, 182-195

Abstract: Abstract In this paper generalizations of Heilbronn’s triangle problem to convex hulls of j points in the unit square [0,1]2 are considered. By using results on the independence number of linear hypergraphs, for fixed integers k≥3 and any integers n≥k a deterministic o(n 6k−4) time algorithm is given, which finds distributions of n points in [0,1]2 such that, simultaneously for j=3,…,k, the areas of the convex hulls determined by any j of these n points are Ω((log n)1/(j−2)/n (j−1)/(j−2)).

Keywords: Heilbronn’s triangle problem; Approximation algorithm; Hypergraphs (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10878-008-9168-7

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