A Deterministic Polynomial-Time Algorithm for Heilbronn's Problem in Three Dimensions
SIAM Journal on Computing
An Algorithm for Heilbronn's Problem
SIAM Journal on Computing
A Lower Bound for Heilbronn's Triangle Problem in d Dimensions
SIAM Journal on Discrete Mathematics
On Heilbronn’s Problem in Higher Dimension
Combinatorica
An Upper Bound for the d-Dimensional Analogue of Heilbronn's Triangle Problem
SIAM Journal on Discrete Mathematics
Large triangles in the d-dimensional unit cube
Theoretical Computer Science - Computing and combinatorics
The On-Line Heilbronn's Triangle Problem in d Dimensions
Discrete & Computational Geometry
Distributions of points in the unit square and large k-gons
European Journal of Combinatorics
Distributions of Points in d Dimensions and Large k-Point Simplices
Discrete & Computational Geometry
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For given integers d,j=2 and any positive integers n, distributions of n points in the d-dimensional unit cube [0,1]^d are investigated, where the minimum volume of the convex hull determined by j of these n points is large. In particular, for fixed integers d,k=2 the existence of a configuration of n points in [0,1]^d is shown, such that, simultaneously for j=2,...,k, the volume of the convex hull of any j points among these n points is @W(1/n^(^j^-^1^)^/^(^1^+^|^d^-^j^+^1^|^)). Moreover, a deterministic algorithm is given achieving this lower bound, provided that d+1@?j@?k.