Hardness results on Voronoi, Laguerre and Apollonius diagrams

International audienceWe show that converting Apollonius and Laguerre diagrams from an already built Delaunay triangulation of a set of n points in 2D requires at least Ω(n log n) computation time. We also show that converting an Apollonius diagram of a set of n weighted points in 2D from a Laguerre diagram and vice-versa requires at least Ω(n log n) computation time as well. Furthermore , we present a very simple randomized incremental construction algorithm that takes expected O(n log n) computation time to build an Apollonius diagram of non-overlapping circles in 2D

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

Hardness results on voronoi, laguerre and apollonius diagrams

We show that converting Apollonius and Laguerre diagrams from an already built Delaunay triangulation of a set of n points in 2D requires at least (n log n) computation time. We also show that converting an Apollonius diagram of a set of n weighted points in 2D from a Laguerre diagram and vice-versa requires at least (n log n) computation time as well. Furthermore, we present a very simple randomized incremental construction algorithm that takes expected O(n log n) computation time to build an Apollonius diagram of non-overlapping circles in 2D.</p

Hardness results on Voronoi, Laguerre and Apollonius diagrams

International audienceWe show that converting Apollonius and Laguerre diagrams from an already built Delaunay triangulation of a set of n points in 2D requires at least Ω(n log n) computation time. We also show that converting an Apollonius diagram of a set of n weighted points in 2D from a Laguerre diagram and vice-versa requires at least Ω(n log n) computation time as well. Furthermore , we present a very simple randomized incremental construction algorithm that takes expected O(n log n) computation time to build an Apollonius diagram of non-overlapping circles in 2D

Hardness results on voronoi, laguerre and apollonius diagrams

We show that converting Apollonius and Laguerre diagrams from an already built Delaunay triangulation of a set of n points in 2D requires at least (n log n) computation time. We also show that converting an Apollonius diagram of a set of n weighted points in 2D from a Laguerre diagram and vice-versa requires at least (n log n) computation time as well. Furthermore, we present a very simple randomized incremental construction algorithm that takes expected O(n log n) computation time to build an Apollonius diagram of non-overlapping circles in 2D