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Optimizing the Layout of Proportional Symbol Maps [chapter]

Guilherme Kunigami, Pedro J. de Rezende, Cid C. de Souza, Tallys Yunes
2011 Lecture Notes in Computer Science  
Proportional symbol maps are a cartographic tool to assist in the visualization and analysis of quantitative data associated with specific locations (e.g. earthquake magnitudes, oil well production, temperature at weather stations, etc.). As the name suggests, symbol sizes are proportional to the magnitude of the physical quantities that they represent. We present a novel integer linear programming model to draw opaque disks on a map with the objective of maximizing the total visible border of
more » ... visible border of all disks (an established measure of quality). In particular, 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 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.
doi:10.1007/978-3-642-21931-3_1 fatcat:uczfueocbzcg7f32pxcxyrtq5m

Generating optimal drawings of physically realizable symbol maps with integer programming

Guilherme Kunigami, Pedro J. de Rezende, Cid C. de Souza, Tallys Yunes
2012 The Visual Computer  
Guilherme Kunigami is a software engineer working with Operations Research.  ... 
doi:10.1007/s00371-012-0727-7 fatcat:hciuy6ejtbgyxag7zh666uwtna

Optimizing the Layout of Proportional Symbol Maps: Polyhedra and Computation

Guilherme Kunigami, Pedro J. de Rezende, Cid C. de Souza, Tallys Yunes
2014 INFORMS journal on computing  
Guilherme Kunigami, Pedro J. de Rezende, Cid C. de Souza Institute of Computing, University of Campinas, Campinas, SP 13083-852, Brazil,, {rezende, cid} Tallys Yunes  ...  An earlier and much shorter version of some of the results herein, not including our latest and best results, appeared as Kunigami et al. (2011) .  ... 
doi:10.1287/ijoc.2013.0557 fatcat:lzjniqjuejhe7jqupjmm34zkyu

A hybrid GRASP heuristic to construct effective drawings of proportional symbol maps

Rafael G. Cano, Guilherme Kunigami, Cid C. de Souza, Pedro J. de Rezende
2013 Computers & Operations Research  
As observed by Kunigami et al. [4] , instance City 156 can be decomposed into relatively small components and, for that reason, it presented no difficulties.  ...  Moreover, the results reported in Kunigami et al. [4] show that solving the Max-Total problem with real-world instances to optimality may require several hours of computation.  ... 
doi:10.1016/j.cor.2012.09.007 fatcat:oa24q5wqgvdvraibsqnnxx7fgq

Determining an Optimal Visualization of Physically Realizable Symbol Maps

Guilherme Kunigami, Pedro Rezende, Cid Souza, Tallys Yunes
2011 2011 24th SIBGRAPI Conference on Graphics, Patterns and Images  
Proportional symbol maps are an often used tool to aid cartographers and geo-science professionals to visualize data associated with events (e.g., earthquakes) or geo-positioned statistical data (e.g., population). At specific locations, symbols are placed and scaled so that their areas become proportional to the magnitudes of the events or data. Recent work approaches the problem of drawing these symbols algorithmically and defines metrics to be optimized to attain different kinds of drawings.
more » ... kinds of drawings. We focus specifically on optimizing the visualization of physically realizable drawings of opaque disks by maximizing the sum of the visible borders of such disks. As this problem has been proven to be NP-hard, we provide an integer programming model for its solution along with decomposition techniques designed to decrease the size of input instances. We present computational experiments to assess the performance of our model as well as the effectiveness of our decomposition techniques.
doi:10.1109/sibgrapi.2011.12 dblp:conf/sibgrapi/KunigamiRSY11 fatcat:sbjugkcydjhannbkty3nkmoony


Savienne Maria Fiorentini Elerbrock Zorn, Guilherme Arantes Pedro, Mateus Souza Amaral, Carla Cristina Almeida Loures, Messias Borges Silva
2017 Holos  
Umas dessas técnicas é a utilização do ultrassom, que pode elevar em mais de 50% o teor de lipídios extraídos da biomassa (Dos Santos, Moreira, Kunigami, Aranda, & Teixeira, 2015; Garoma & Janda, 2016  ... 
doi:10.15628/holos.2017.5655 fatcat:bbqbp6tfh5epvkixouqagpljx4