Optimizing the layout of proportional symbol maps

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


Proportional symbol maps are a cartographic tool to assist in the visualization and analysis of quantitative data associated with specific locations (earthquake magnitudes, oil well production, temperature at weather stations, etc.). Symbol sizes are proportional to the magnitude of the quantities that they represent. We present a novel integer programming model to draw opaque disks on a map with the objective of maximizing the total visible border of all disks (an established measure of quality). We focus on drawings obtained by layering symbols on top of each other, known as stacking drawings. We introduce decomposition techniques, and several new families of facet-defining inequalities, which are implemented in a cut-and-branch algorithm. We assess the effectiveness of our approach through a series of computational experiments using real demographic and geophysical data. To the best of our knowledge, we are the first to provide provably optimal solutions to some of those problem instances.

Original languageEnglish (US)
Title of host publicationComputational Science and Its Applications, ICCSA 2011 - International Conference, Proceedings
Number of pages16
EditionPART 3
StatePublished - 2011
Event2011 International Conference on Computational Science and Its Applications, ICCSA 2011 - Santander, Spain
Duration: Jun 20 2011Jun 23 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 3
Volume6784 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other2011 International Conference on Computational Science and Its Applications, ICCSA 2011


  • Cartography
  • Computational Geometry
  • Integer Linear Programming
  • Symbol Maps

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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