Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cabello, S., Haverkort, H., van Kreveld, M., Speckmann, B.: Algorithmic aspects of proportional symbol maps. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 720–731. Springer, Heidelberg (2006)
Cabello, S., Haverkort, H., van Kreveld, M., Speckmann, B.: Algorithmic aspects of proportional symbol maps. Algorithmica 58(3), 543–565 (2010)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Fair Isaac Corporation. Xpress Optimizer Reference Manual (2009)
Dent, B.: Cartography – Thematic Map Design, 5th edn. McGraw-Hill, New York (1999)
Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, San Francisco (1979)
Griffin, T.: The importance of visual contrast for graduated circles. Cartography 19(1), 21–30 (1990)
Kunigami, G., de Rezende, P.J., de Souza, C.C., Yunes, T.: Optimizing the layout of proportional symbol maps (2010), http://www.optimization-online.org/DB_HTML/2010/11/2805.html
Nemhauser, G.L., Sigismondi, G.: A strong cutting plane/branch-and-bound algorithm for node packing. Journal of the Operational Research Society 43(5), 443–457 (1992)
Nemhauser, G.L., Wolsey, L.A.: Integer and combinatorial optimization. Wiley-Interscience, New York (1988)
NOAA Satellite and Information Service. National geophysical data center (2005), http://www.ngdc.noaa.gov
Slocum, T.A., McMaster, R.B., Kessler, F.C., Howard, H.H.: Thematic Cartography and Geographic Visualization, 2nd edn. Prentice-Hall, Englewood Cliffs (2003)
Wein, R., Fogel, E., Zukerman, B., Halperin, D.: Advanced programming techniques applied to CGAL’s arrangement package. Computational Geometry 38(1-2), 37–63 (2007), http://www.cgal.org
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kunigami, G., de Rezende, P.J., de Souza, C.C., Yunes, T. (2011). Optimizing the Layout of Proportional Symbol Maps. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21931-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-21931-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21930-6
Online ISBN: 978-3-642-21931-3
eBook Packages: Computer ScienceComputer Science (R0)