Weight-proportional Space Partitioning Using Adaptive Voronoi Diagrams
Traditional application of Voronoi diagrams for space partitioning results in Voronoi regions, each with a specific area determined by the generators 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 boundaries using quadtree decomposition. We present the corresponding algorithm and its complexity analysis. The method is successfully tested on a series of idealtypical cases and the interactions between the adaptive technique and boundary resolution refinement are explored and assessed.
space partitioning voronoi diagrams information space optimization fixed-point iteration spatial resolution quadtree decomposition adaptive algorithm areaweight proportional algorithm complexity