A New Approach to Output-Sensitive Construction of Voronoi Diagrams and Delaunay Triangulations
| Autor: | Donald R. Sheehy, Gary L. Miller |
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| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Delaunay triangulation Lloyd's algorithm Weighted Voronoi diagram Theoretical Computer Science Bowyer–Watson algorithm Combinatorics Fortune's algorithm Computational Theory and Mathematics TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Discrete Mathematics and Combinatorics Power diagram Geometry and Topology Voronoi diagram Centroidal Voronoi tessellation Mathematics |
| Zdroj: | Discrete & Computational Geometry. 52:476-491 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-014-9629-y |
| Popis: | We describe a new algorithm for computing the Voronoi diagram of a set of $$n$$n points in constant-dimensional Euclidean space. The running time of our algorithm is $$O(f \log n \log \varDelta )$$O(flognlogΔ) where $$f$$f is the output complexity of the Voronoi diagram and $$\varDelta $$Δ is the spread of the input, the ratio of largest to smallest pairwise distances. Despite the simplicity of the algorithm and its analysis, it improves on the state of the art for all inputs with polynomial spread and near-linear output size. The key idea is to first build the Voronoi diagram of a superset of the input points using ideas from Voronoi refinement mesh generation. Then, the extra points are removed in a straightforward way that allows the total work to be bounded in terms of the output complexity, yielding the output sensitive bound. The removal only involves local flips and is inspired by kinetic data structures. |
| Databáze: | OpenAIRE |
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