Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Efficient algorithms for common transversals
Information Processing Letters
Stabbing pairwise disjoint translates in linear time
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Algorithms for high dimensional stabbing problems
Discrete Applied Mathematics - Computational combinatiorics
The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n - 2
Discrete & Computational Geometry
Discrete & Computational Geometry
Bounding the number of geometric permutations induced by k-transversals
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
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We show that the maximum combinatorial complexity of the space of hyperplane transversals to a family of n separated and strictly convex sets in Rd is &THgr;(n⌊d/2⌋), which generalizes results of Edelsbrunner and Sharir in the plane. As a key step in the argument, we show that the space of hyperplanes tangent to &kgr; ≤ d separated and strictly convex sets in Rd is a topological (d - &kgr;)-sphere.