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Journal of the ACM (JACM)
There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
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Advances in Applied Mathematics
Approximating the complete Euclidean graph
No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
Voronoi diagrams with barriers and the shortest diagonal problem
Information Processing Letters
An optimal synchronizer for the hypercube
SIAM Journal on Computing
Proceedings of the international symposium on Optimal algorithms
Which triangulations approximate the complete graph?
Proceedings of the international symposium on Optimal algorithms
Construction of three-dimensional Delaunay triangulations using local transformations
Computer Aided Geometric Design
Optimal parallel algorithms for triangulated simple polygons
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Quality mesh generation in three dimensions
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
The minimum perimeter polygon and its application
Proceedings of the 6th Workshop on Theoretical Foundations of Computer Vision
The Delauney Triangulation Closely Approximates the Complete Euclidean Graph
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Voronoi Diagrams for Moving Disks and Applications
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
STAR-Tree: An Efficient Self-Adjusting Index for Moving Objects
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Geometrically aware communication in random wireless networks
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Kinetic and dynamic data structures for convex hulls and upper envelopes
Computational Geometry: Theory and Applications
A simple and efficient kinetic spanner
Proceedings of the twenty-fourth annual symposium on Computational geometry
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
A simple and efficient kinetic spanner
Computational Geometry: Theory and Applications
Geodesic Spanners on Polyhedral Surfaces
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
An approximation algorithm for computing minimum-length polygons in 3D images
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part IV
Shortest paths in a cuboidal world
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Kinetic data structures for all nearest neighbors and closest pair in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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It is well known that the Delaunay Triangulation is a spanner graph of its vertices. In this paper we show that any bounded aspect ratio triangulation in two and three dimensions is a spanner graph of its vertices as well. We extend the notion of spanner graphs to environments with obstacles and show that both the Constrained Delaunay Triangulation and bounded aspect ratio conforming triangulations are spanners with respect to the corresponding visibility graph. We also show how to kinetize the Constrained Delaunay Triangulation. Using such time-varying triangulations we describe how to maintain sets of near neighbors for a set of moving points in both unconstrained and constrained environments. Such nearest neighbor maintenance is needed in many virtual environments where nearby agents interact. Finally, we show how to use the Constrained Delaunay Triangulation in order to maintain the relative convex hull of a set of points moving inside a simple polygon.