@article {1974516,
	title = {Weight-proportional Space Partitioning Using Adaptive Voronoi Diagrams},
	journal = {Geoinformatica},
	volume = {11},
	year = {2007},
	month = {2007},
	pages = {383-405},
	abstract = {Traditional application of Voronoi diagrams for space partitioning results in Voronoi regions, each with a specific area determined by the generators{\textquoteright} relative locations and weights. Particularly in the area of information space (re)construction, however, there is a need for inverse solutions; i.e., finding weights that result in regions with predefined area ratios. In this paper, we formulate an adaptive Voronoi solution and propose a raster-based optimization method for finding the associated weight set. The solution consists of a combination of simple, fixed-point iteration with an optional spatial resolution refinement along the regions{\textquoteright} boundaries using quadtree decomposition. We present the corresponding algorithm and its complexity analysis. The method is successfully tested on a series of ideal{\textquotedblright}typical cases and the interactions between the adaptive technique and boundary resolution refinement are explored and assessed.},
	keywords = {BIS},
	author = {Reitsma,Reindert and Trubin,S, and Mortensen,E.}
}
