Generating optimal drawings of physically realizable symbol maps with integer programming

Guilherme Kunigami, Pedro J. De Rezende, Cid C. De Souza, Tallys Yunes

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 quality 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.

Original languageEnglish (US)
Pages (from-to)1015-1026
Number of pages12
JournalVisual Computer
Issue number10
StatePublished - Oct 2012


  • Cartography
  • Computational geometry
  • Integer linear programming
  • Visualization

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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