Orphan-Free Anisotropic Voronoi Diagrams
  We describe conditions under which an appropriately-defined anisotropic Voronoi diagram of a set of sites in Euclidean space is guaranteed to be composed of connected cells in any number of dimensions. These conditions are natural for problems in optimization and approximation, and algorithms already exist to produce sets of sites that satisfy them. 
Guillermo D. Canas and Steven J. Gortler
cs.CG