A sweepline algorithm for Voronoi diagrams
SCG '86 Proceedings of the second annual symposium on Computational geometry
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
On the construction of abstract Voronoi diagrams
Discrete & Computational Geometry
Randomized incremental construction of abstract Voronoi diagrams
Computational Geometry: Theory and Applications
Improved incremental randomized Delaunay triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Voronoi Diagram of a Circle Set Constructed from Voronoi Diagram of a Point Set
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Proximity structures for moving objects in constrained and unconstrained environments
Proximity structures for moving objects in constrained and unconstrained environments
Root comparison techniques applied to computing the additively weighted Voronoi diagram
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The predicates of the Apollonius diagram: algorithmic analysis and implementation
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Dynamic label placement for improved interactive exploration
NPAR '08 Proceedings of the 6th international symposium on Non-photorealistic animation and rendering
Single facility collection depots location problem in the plane
Computational Geometry: Theory and Applications
The predicates of the Apollonius diagram: Algorithmic analysis and implementation
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Convex hull and voronoi diagram of additively weighted points
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Using Voronoi diagrams to solve a hybrid facility location problem with attentive facilities
Information Sciences: an International Journal
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In this paper we present a dynamic algorithm for the construction of the additively weighted Voronoi diagram of a set of weighted points in the plane. The novelty in our approach is that we use the dual of the additively weighted Voronoi diagram to represent it. This permits us to perform both insertions and deletions of sites easily. Given a set B of n sites, among which h sites have a non-empty cell, our algorithm constructs the additively weighted Voronoi diagram of B in O(nT(h) + h log h) expected time, where T(k) is the time to locate the nearest neighbor of a query site within a set of k sites. Deletions can be performed for all sites whether or not their cell is empty. The space requirements for the presented algorithm is O(n). Our algorithm is simple to implement and experimental results suggest an O(n log h) behavior.