On farthest Bregman Voronoi cells

Let g be a strictly convex function on an evenly convex set X⊂Rn with nonempty interior. Assuming that g is differentiable on intX, we consider the Bregman distance Dg associated with g. Given a set T ⊂Rn, whose elements are called sites, and a particular site s, the farthest g-Bregman Voronoi cell of s, denoted by FTg(s), consists of all points that are farther from s than from any other site with respect to Dg. In this paper we study farthest g-Bregman Voronoi cells; in particular, we characterize those sets that can be written as FTg(s) for some T⊂Rn and some s∈T.