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In this paper we study the Voronoi diagram for a set of N line segments and circles in the Euclidean plane. The diagram is a generalization of the Voronoi diagram for a set of points in the plane and has applications in wire layout, facility location, clustering and contouring problems. We present an O (N (N) ²) algorithm for constructing the diagram. It is an improvement of a previous known result which takes O (Nc^ { N }) time. The algorithm described in this paper is also shown to be applicable under a more general metric if certain conditions are satisfied.
Lee et al. (Sun,) studied this question.