eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-08-26
45:1
45:18
10.4230/LIPIcs.ESA.2020.45
article
Linear Expected Complexity for Directional and Multiplicative Voronoi Diagrams
Fan, Chenglin
1
Raichel, Benjamin
1
Department of Computer Science, University of Texas at Dallas, Richardson, TX, USA
While the standard unweighted Voronoi diagram in the plane has linear worst-case complexity, many of its natural generalizations do not. This paper considers two such previously studied generalizations, namely multiplicative and semi Voronoi diagrams. These diagrams both have quadratic worst-case complexity, though here we show that their expected complexity is linear for certain natural randomized inputs. Specifically, we argue that the expected complexity is linear for: (1) semi Voronoi diagrams when the visible direction is randomly sampled, and (2) for multiplicative diagrams when either weights are sampled from a constant-sized set, or the more challenging case when weights are arbitrary but locations are sampled from a square.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol173-esa2020/LIPIcs.ESA.2020.45/LIPIcs.ESA.2020.45.pdf
Voronoi Diagrams
Expected Complexity
Computational Geometry