Abstract
Proportional symbol maps visualize numerical data associated with point locations by placing a scaled symbol—typically opaque disks or squares—at the corresponding point on a map. Overlapping symbols need to be drawn in such a way that the user can still judge their relative sizes accurately.
We identify two types of suitable drawings: physically realizable drawings and stacking drawings. For these we study the following two problems: Max-Min—maximize the minimum visible boundary length of each symbol—and Max-Total—maximize the total visible boundary length over all symbols. We show that both problems are NP-hard for physically realizable drawings. Max-Min can be solved in O(n 2logn) time for stacking drawings, which can be improved to O(nlogn) or O(nlog2 n) time when the input has certain properties. We also experimented with four methods to compute stacking drawings: our solution to the Max-Min problem performs best on the data sets considered.
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References
Agarwal, P.K., Suri, S.: Surface approximation and geometric partitions. SIAM J. Comput. 27, 1016–1035 (1998)
Clarke, K.C.: Analytical and Computer Cartography, 2nd edn. Prentice Hall, Englewood Cliffs (1995)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications, 2nd edn. Springer, Berlin (2000)
Demaine, E.D., Mitchell, J.S.B., O’Rourke, J.: The open problems project. Problem 33, http://maven.smith.edu/~orourke/TOPP/P33.html
Dent, B.: Cartography - thematic map design, 5th edn. McGraw-Hill, New York (1999)
Fortnow, L: Computational Complexity Blog (post of Friday, February 14, 2003), http://weblog.fortnow.com/archive/2003_02_01_archive.html
Fowler, R.J., Paterson, M.S., Tanimoto, S.L.: Optimal packing and covering in the plane are NP-complete. Inform. Process. Lett. 12(3), 133–137 (1981)
Griffin, T.: The importance of visual contrast for graduated circles. Cartography 19(1), 21–30 (1990)
Knuth, D.E., Raghunathan, A.: The problem of compatible representatives. SIAM J. Discrete Math. 5, 422–427 (1992)
Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11(2), 329–343 (1982)
NOAA Satellite and Information Service. National geophysical data center (2005), http://www.ngdc.noaa.gov/
Queensland University Advanced Centre for Earthquake Studies, http://www.quakes.uq.edu.au
Slocum, T.A., McMaster, R.B., Kessler, F.C., Howard, H.H.: Thematic Cartography and Geographic Visualization, 2nd edn. Prentice-Hall, Englewood Cliffs (2003)
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© 2006 Springer-Verlag Berlin Heidelberg
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Cabello, S., Haverkort, H., van Kreveld, M., Speckmann, B. (2006). Algorithmic Aspects of Proportional Symbol Maps. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_64
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DOI: https://doi.org/10.1007/11841036_64
Publisher Name: Springer, Berlin, Heidelberg
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