The average-case area of Heilbronn-type triangles
Random Structures & Algorithms
A Deterministic Polynomial Time Algorithm for Heilbronn's Problem in Dimension Three
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
The On-Line Heilbronn's Triangle Problem in Three and Four Dimensions
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Distributions of points in the unit-square and large k-gons
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Large triangles in the d-dimensional unit cube
Theoretical Computer Science - Computing and combinatorics
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Distributions of points in the unit square and large k-gons
European Journal of Combinatorics
Convex Hulls of Point-Sets and Non-uniform Hypergraphs
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Generalizations of Heilbronn's triangle problem
European Journal of Combinatorics
Point sets in the unit square and large areas of convex hulls of subsets of points
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Distributions of points and large convex hulls of k points
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Distributions of points in d dimensions and large k-point simplices
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
The on-line heilbronn’s triangle problem in d dimensions
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Distributions of points and large quadrangles
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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In this paper we show a lower bound for the generalization of Heilbronn's triangle problem to d dimensions; namely, we show that there exists a set S of n points in the d-dimensional unit cube so that every d+1 points of S define a simplex of volume $\Omega (\frac{1}{n^d})$. We also show a constructive incremental positioning of n points in a unit 3-cube for which every tetrahedron defined by four of these points has volume $\Omega (\frac{1}{n^4})$.