Farthest-point Voronoi diagrams in the presence of rectangular obstacles
We present an algorithm to compute the geodesic L_1 farthest-point Voronoi diagram of m point sites in the presence of n rectangular obstacles in the plane. It takes O(nm+n log n + mlog m) construction time using O(nm) space. This is the first optimal algorithm for constructing the farthest-point Voronoi diagram in the presence of obstacles. We can construct a data structure in the same construction time and space that answers a farthest-neighbor query in O(log(n+m)) time.
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