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Lower Bounds for the Complexity of the Voronoi Diagram of Polygonal Curves under the Discrete Frechet Distance (0708.1909v1)
Published 14 Aug 2007 in cs.CG and cs.CC
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(n{dk}) for dimension d=1,2 and Omega(n{d(k-1)+2}) for d>2.