Point Sets in the Unit Square and Large Areas of Convex Hulls of Subsets of Points
نویسنده
چکیده
In this paper generalizations of Heilbronn's triangle problem are considered. By using results on the independence number of linear hypergraphs, for xed integers k 3 and any integers n k a o(n6k 4) time deterministic algorithm is given, which nds 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 ((logn)1=(j 2)=n(j 1)=(j 2)).
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