Lower Bounds for the Complexity of the Voronoi Diagram of Polygonal Curves under the Discrete Frechet Distance
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 Rd with k vertices each, has complexity Omega(ndk) for dimension d=1,2 and Omega(nd(k-1)+2) for d>2.
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