OPTIMAL CONSTRUCTION OF THE CITY VORONOI DIAGRAM

Abstract

We address proximity problems in the presence of roads on the L-1 plane. More specifically, we present the first optimal algorithm for constructing the city Voronoi diagram. We apply the continuous Dijkstra method to obtain an optimal algorithm for building a shortest path map for a given source, and then it extends to that for the city Voronoi diagram. Moreover, our algorithm can be extended to other generalized situations including metric spaces induced by roads and obstacles together.