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arXiv · 2004.09385

Linear Expected Complexity for Directional and Multiplicative Voronoi Diagrams

Chenglin Fan·Benjamin Raichel
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Abstract

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.

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Chenglin Fan, Benjamin Raichel. 2020-04-20. Linear Expected Complexity for Directional and Multiplicative Voronoi Diagrams. https://arxiv.org/abs/2004.09385

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