### Abstract

Proportional symbol maps are a cartographic tool to assist in the visualization and analysis of quantitative data associated with specific locations, such as earthquake magnitudes, oil well production, and temperature at weather stations. As the name suggests, symbol sizes are proportional to the magnitude of the physical quantities that they represent. We present two novel integer linear programming (ILP) models to solve this computational geometry problem: how to draw opaque disks on a map so as to maximize the total visible border of all disks. We focus on drawings obtained by layering symbols on top of each other, also known as stacking drawings. We introduce decomposition techniques as well as several families of facet-defining inequalities, which are used to strengthen the ILP models that are supplied to a commercial solver. We demonstrate the effectiveness of our approach through a series of computational experiments using hundreds of instances generated from real demographic and geophysical data sets. To the best of our knowledge, we are the first to use ILP to tackle this problem, and the first to provide provably optimal symbol maps for those data sets.

Original language | English (US) |
---|---|

Pages (from-to) | 199-207 |

Number of pages | 9 |

Journal | INFORMS Journal on Computing |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2014 |

### Fingerprint

### Keywords

- Cartography
- Computational geometry
- Integer programming
- Symbol maps

### ASJC Scopus subject areas

- Software
- Information Systems
- Computer Science Applications
- Management Science and Operations Research

### Cite this

*INFORMS Journal on Computing*,

*26*(2), 199-207. https://doi.org/10.1287/ijoc.2013.0557

**Optimizing the layout of proportional symbol maps : Polyhedra and computation.** / Kunigami, Guilherme; De Rezende, Pedro J.; De Souza, Cid C.; Yunes, Tallys.

Research output: Contribution to journal › Article

*INFORMS Journal on Computing*, vol. 26, no. 2, pp. 199-207. https://doi.org/10.1287/ijoc.2013.0557

}

TY - JOUR

T1 - Optimizing the layout of proportional symbol maps

T2 - Polyhedra and computation

AU - Kunigami, Guilherme

AU - De Rezende, Pedro J.

AU - De Souza, Cid C.

AU - Yunes, Tallys

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Proportional symbol maps are a cartographic tool to assist in the visualization and analysis of quantitative data associated with specific locations, such as earthquake magnitudes, oil well production, and temperature at weather stations. As the name suggests, symbol sizes are proportional to the magnitude of the physical quantities that they represent. We present two novel integer linear programming (ILP) models to solve this computational geometry problem: how to draw opaque disks on a map so as to maximize the total visible border of all disks. We focus on drawings obtained by layering symbols on top of each other, also known as stacking drawings. We introduce decomposition techniques as well as several families of facet-defining inequalities, which are used to strengthen the ILP models that are supplied to a commercial solver. We demonstrate the effectiveness of our approach through a series of computational experiments using hundreds of instances generated from real demographic and geophysical data sets. To the best of our knowledge, we are the first to use ILP to tackle this problem, and the first to provide provably optimal symbol maps for those data sets.

AB - Proportional symbol maps are a cartographic tool to assist in the visualization and analysis of quantitative data associated with specific locations, such as earthquake magnitudes, oil well production, and temperature at weather stations. As the name suggests, symbol sizes are proportional to the magnitude of the physical quantities that they represent. We present two novel integer linear programming (ILP) models to solve this computational geometry problem: how to draw opaque disks on a map so as to maximize the total visible border of all disks. We focus on drawings obtained by layering symbols on top of each other, also known as stacking drawings. We introduce decomposition techniques as well as several families of facet-defining inequalities, which are used to strengthen the ILP models that are supplied to a commercial solver. We demonstrate the effectiveness of our approach through a series of computational experiments using hundreds of instances generated from real demographic and geophysical data sets. To the best of our knowledge, we are the first to use ILP to tackle this problem, and the first to provide provably optimal symbol maps for those data sets.

KW - Cartography

KW - Computational geometry

KW - Integer programming

KW - Symbol maps

UR - http://www.scopus.com/inward/record.url?scp=84899474975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899474975&partnerID=8YFLogxK

U2 - 10.1287/ijoc.2013.0557

DO - 10.1287/ijoc.2013.0557

M3 - Article

AN - SCOPUS:84899474975

VL - 26

SP - 199

EP - 207

JO - INFORMS Journal on Computing

JF - INFORMS Journal on Computing

SN - 1091-9856

IS - 2

ER -