STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Data structures for mobile data
Journal of Algorithms
Swap conditions for dynamic Voronoi diagrams for circles and line segments
Computer Aided Geometric Design
Kinetic connectivity for unit disks
Proceedings of the sixteenth annual symposium on Computational geometry
Static and kinetic geometric spanners with applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Robot Motion Planning
Compact Voronoi Diagrams for Moving Convex Polygons
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
Probabilistic Voronoi diagrams for probabilistic moving nearest neighbor queries
Data & Knowledge Engineering
UV-diagram: a voronoi diagram for uncertain spatial databases
The VLDB Journal — The International Journal on Very Large Data Bases
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In this paper we discuss the kinetic maintenance of the Euclidean Voronoi diagram and its dual, the Delaunay triangulation, for a set of moving disks. The most important aspect in our approach is that we can maintain the Voronoi diagram even in the case of intersecting disks. We achieve that by augmenting the Delaunay triangulation with some edges associated with the disks that do not contribute to the Voronoi diagram. Using the augmented Delaunay triangulation of the set of disks as the underlying structure, we discuss how to maintain, as the disks move, (1) the closest pair, (2) the connectivity of the set of disks and (3) in the case of non-intersecting disks, the near neighbors of a disk.