Farthest-Point Voronoi Diagrams in the Presence of Rectangular Obstacles

초록

We present an algorithm to compute the geodesic L1 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 + m log 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.