Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
On the number of halving planes
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Points and triangles in the plane and halving planes in space
Discrete & Computational Geometry
Cutting dense point sets in half
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
On geometric optimization with few violated constraints
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
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Every collection of t ≥ 2n2 triangles witha total of n vertices in R3 has Wt4n6 crossing pairs. This implies that one of their edgesmeetsWt3n6 of the triangles. From this it followsthat n points in R3 have only O(n8/3) halvingplanes.