Proportional symbol maps are a tool often used by cartographers and geoscience professionals to visualize geopositioned data associated with events and demographic statistics, such as earthquakes and population counts. Symbols are placed at specific locations on a map, and their areas are scaled to become proportional to the magnitudes of the data points they represent. We focus specifically on creating physically realizable drawings of symbols-opaque disks, in our case-by maximizing two

more »

... metrics: the total and the minimum length of their visible borders. As these two maximization problems have been proven to be NPhard, we provide integer programming formulations for their solution, along with decomposition techniques designed to decrease the size of input instances. Our computational experiments, which use real-life data sets, demonstrate the effectiveness of our approach and provide, for the first time, a number of optimal solutions to previously studied instances of this problem. Guilherme Kunigami is a software engineer working with Operations Research. His research interests are in combinatorial optimization (including integer linear programming and metaheuristics), artificial intelligence, computational geometry, and computer graphics. He holds a M.Sc. degree in Computer Science and B.S. degree in Computer Engineering from the University of Campinas, Brazil.