Voronoi diagrams with a transportation network on the Euclidean plane

Abstract

This paper investigates geometric and algorithmic properties of the Voronoi diagram with a transportation network on the Euclidean plane. With a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm(2) log n + m(3) log m) algorithm to compute the Voronoi diagram with a transportation network on the Euclidean plane, where n is the number of given sites and m is the complexity of the given transportation network.