AN ABSTRACT OF THE THESIS OF Stanislav I

approved: _____________________________________________________________________ E. N. Mortensen R. F. Reitsma Traditional application of Voronoi diagrams for space partitioning creates Voronoi regions, with areas determined by the generators’ relative locations and weights. Especially 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 areas. In this thesis, an Adaptive Multiplicatively Weighted Voronoi Diagram solution is formulated and a raster-based optimization method for finding the associated weight set is proposed. The basic algorithm is described, and several improvements are explored in detail, followed by algorithm’s complexity analysis. The adaptive solution is successfully tested is successfully tested on a series of ideal/pathological cases, as well as using empirical data.