Lower Bounds for the Complexity of the Voronoi Diagram of Polygonal Curves under the Discrete Frechet Distance

Details Lower Bounds for the Complexity of the Voronoi Diagram of Polygonal Curves under the Discrete Frechet Distance Lower Bounds for the Complexity of the Voronoi Diagram of Polygonal Curves under the Discrete Frechet Distance

2007-08-14

arxiv.org/abs/0708.1909v1

Computer Science

Computational Geometry

6 pages, 2 figures

Scientific paper

We give lower bounds for the combinatorial complexity of the Voronoi diagram
of polygonal curves under the discrete Frechet distance. We show that the
Voronoi diagram of n curves in R^d with k vertices each, has complexity
Omega(n^{dk}) for dimension d=1,2 and Omega(n^{d(k-1)+2}) for d>2.

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