I. Introduction
The notion of the Voronoi diagram of a finite set of points in a Euclidean space is a rich concept with numerous applications. For a survey of results on Voronoi diagrams, see [3]. Voronoi diagrams have given rise to many variations. One of these, the zone diagram defined by Asano, et al. [2], is a new and rich variation of the Voronoi diagram for a given finite set of points in the Euclidean plane. The notion of a zone diagram and its existence was the main motivation behind defining mollified versions in [1], called territory diagrams and maximal territory diagrams. However, the study was also motivated by an intriguing relationship between approximations to Voronoi diagrams and certain regions of attraction in polynomial root-finding through iterations [4], [5].