Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams

@article{Guibas1983PrimitivesFT,
  title={Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams},
  author={Leonidas J. Guibas and Jorge Stolfi},
  journal={Proceedings of the fifteenth annual ACM symposium on Theory of computing},
  year={1983}
}
  • L. Guibas, J. Stolfi
  • Published 1 December 1983
  • Computer Science
  • Proceedings of the fifteenth annual ACM symposium on Theory of computing
We discuss the following problem: given n points in the plane (the “sites”), and an arbitrary query point q, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites, and then locating the query point in one of its regions. We give two algorithms, one that constructs the Voronoi diagram in O(n lg n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, the Delaunay triangulation, and… 
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