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STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On the number of faces in higher-dimensional Voronoi diagrams
SCG '87 Proceedings of the third annual symposium on Computational geometry
An Algorithm for Convex Polytopes
Journal of the ACM (JACM)
Geometric transforms for fast geometric algorithms
Geometric transforms for fast geometric algorithms
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
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SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Delaunay Triangulation in Three Dimensions
IEEE Computer Graphics and Applications
Reasoning about categories in conceptual spaces
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Geometric minimum spanning trees with GEOFILTERKRUSKAL*
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
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This work is the first to validate theoretically the suspicions of many researchers — that the “average” Voronoi diagram is combinatorially quite simple and can be constructed quickly. Specifically, assuming that dimension d is fixed, and that n input points are chosen independently from the uniform distribution on the unit d-ball, it is proved thatthe expected number of simplices of the dual of the Voronoi diagram is &THgr;(n) (exact constants are derived for the high-order term), anda relatively simple algorithm exists for constructing the Voronoi diagram in &THgr;(n) time.It is likely that the methods developed in the analysis will be applicable to other related quantities and other probability distributions.