Weight-proportional Space Partitioning Using Adaptive Voronoi Diagrams

  • Authors:
  • René Reitsma;Stanislav Trubin;Eric Mortensen

  • Affiliations:
  • College of Business, Oregon State University, Corvallis, USA 97331;Electrical Engineering & Computer Science, Oregon State University, Corvallis, USA 97331;School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, USA 97331

  • Venue:
  • Geoinformatica
  • Year:
  • 2007

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Abstract

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 ideal---typical cases and the interactions between the adaptive technique and boundary resolution refinement are explored and assessed.