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arXiv · 0708.1909

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

Kevin Buchin·Maike Buchin
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Abstract

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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Kevin Buchin, Maike Buchin. 2007-08-14. Lower Bounds for the Complexity of the Voronoi Diagram of Polygonal Curves under the Discrete Frechet Distance. https://arxiv.org/abs/0708.1909

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