A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
Crossing Numbers and Hard Erdös Problems in Discrete Geometry
Combinatorics, Probability and Computing
Crossing patterns of semi-algebraic sets
Journal of Combinatorial Theory Series A
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A point set is separated if the minimum distance between its elements is one. Two numbers are called nearly equal if they differ by at most one. If a fixed positive percentage of all pairs of points belonging to a separated set of size n in R^3 determine nearly equal distances, then the diameter of the set is at least constant times n. This proves a conjecture of Erdos.