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

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  • Hanno Lefmann

    (TU Chemnitz)

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)).

Suggested Citation

  • Hanno Lefmann, 2008. "Point sets in the unit square and large areas of convex hulls of subsets of points," Journal of Combinatorial Optimization, Springer, vol. 16(2), pages 182-195, August.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:2:d:10.1007_s10878-008-9168-7
    DOI: 10.1007/s10878-008-9168-7
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