Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Points, spheres, and separators: a unified geometric approach to graph partitioning
Points, spheres, and separators: a unified geometric approach to graph partitioning
Randomized algorithms
Handbook of discrete and computational geometry
Geometry for modeling biomolecules
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
The probabilistic complexity of the Voronoi diagram of points on a polyhedron
Proceedings of the eighteenth annual symposium on Computational geometry
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes
Computational Geometry: Theory and Applications
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
Random Graphs for Statistical Pattern Recognition
Random Graphs for Statistical Pattern Recognition
Dense Point Sets Have Sparse Delaunay Triangulations or “... But Not Too Nasty”
Discrete & Computational Geometry
Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization)
Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization)
Complexity of Delaunay triangulation for points on lower-dimensional polyhedra
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry: Theory and Applications
On the expected complexity of voronoi diagrams on terrains
Proceedings of the twenty-eighth annual symposium on Computational geometry
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We define and study a geometric graph over points in the plane that captures the local behavior of Delaunay triangulations of points on smooth surfaces in IR3. Two points in a planar point set P are neighbors in the empty-ellipse graph if they lie on an axis-aligned ellipse with no point of P in its interior. The empty-ellipse graph can be a clique in the worst case, but it is usually much less dense. Specifically, the empty-ellipse graph of n points has complexity Θ(Δn) in the worst case, where Δ is the ratio between the largest and smallest pairwise distances. For points generated uniformly at random in a rectangle, the empty-ellipse graph has expected complexity Θ(n log n). As an application of our proof techniques, we show that the Delaunay triangulation of n random points on a circular cylinder has expected complexity Θ(n log n).