Realizing Farthest-Point Voronoi Diagrams
نویسندگان
چکیده
1 The farthest-point Voronoi diagram of a set of n sites 2 is a tree with n leaves. We investigate whether arbi3 trary trees can be realized as farthest-point Voronoi di4 agrams. Given an abstract ordered tree T with n leaves 5 and prescribed edge lengths, we produce a set of n sites 6 S in O(n) time such that the farthest-point Voronoi di7 agram of S represents T . We generalize this algorithm 8 to smooth strictly convex symmetric distance functions. 9 Furthermore, when given a subdivision Z of R, we 10 check in linear time whether Z realizes a k-dimensional 11 farthest-point Voronoi diagram when k is a constant. 12
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