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 presence n rectangular obstacles plane. It takes $$O(nm+n \log + m\log m)$$ construction time using O(nm) space. This is first optimal for constructing obstacles. can construct a data structure same and space that answers farthest-neighbor query $$O(\log (n+m))$$ time.