The projector algorithm: A simple parallel algorithm for computing Voronoi diagrams and Delaunay graphs

The Voronoi diagram is a certain geometric data structure which has found numerous applications in various scientific and technological fields. The theory of algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich and useful, with several different and important algorithms. How...

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Veröffentlicht in:Theoretical computer science Jg. 970; S. 114054
1. Verfasser: Reem, Daniel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 29.08.2023
Schlagworte:
Algorithm
Combinatorial representation
Delaunay graph
Parallel computing
Projector
Ray
Subedge
Subwedge
Vertex
Voronoi cell
Voronoi diagram
Wedge
Combinatorial representation
Projector
Vertex
Parallel computing
Voronoi diagram
Subwedge
Delaunay graph
Voronoi cell
Ray
Algorithm
Subedge
Wedge
ISSN:0304-3975, 1879-2294
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Beschreibung
Zusammenfassung:The Voronoi diagram is a certain geometric data structure which has found numerous applications in various scientific and technological fields. The theory of algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich and useful, with several different and important algorithms. However, this theory has been quite steady during the last few decades in the sense that no essentially new algorithms have entered the game. In addition, most of the known algorithms are serial in nature and hence cast inherent difficulties on the possibility to compute the diagram in parallel. In this paper we present the projector algorithm: a new and simple algorithm which enables the (combinatorial) computation of 2D Voronoi diagrams. The algorithm is significantly different from previous ones and some of the involved concepts in it are in the spirit of linear programming and optics. Parallel implementation is naturally supported since each Voronoi cell (actually, even just portions of one cell) can be computed independently of the other cells. A new combinatorial structure for representing the cells (and any convex polytope) is described along the way and the computation of the induced Delaunay graph is obtained almost automatically. •The projector algorithm: a new and simple algorithm for computing 2D Voronoi diagrams.•Each Voronoi cell (or even just parts of it) is computed independently of other ones.•Hence parallel implementation is naturally supported.•The induced Delaunay graph: obtained essentially automatically.•A new combinatorial representation for the cells (and any convex polytope).
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2023.114054