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

Authors:
Hanno Lefmann
Affiliations:
Fakultät für Informatik, TU Chemnitz, Chemnitz, Germany
Venue:
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Year:
2007

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Abstract

In this paper generalizations of Heilbronn's triangle problem are considered. By using results on the independence number of linear hypergraphs, for fixed integers k ≥ 3 and any integers n ≥ k a o(n6k-4) time deterministic algorithm is given, which finds distributions of n points in the unit square [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)).