Evolution Strategies for Optimizing Rectangular Cartograms

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• 作者：Kevin Buchin (20)
  Bettina Speckmann (20)
  Sander Verdonschot (21)
  
• 关键词：Rectangular cartogram ; evolution strategy ; regular edge labeling
• 刊名：Lecture Notes in Computer Science
• 出版年：2012
• 出版时间：2012
• 年：2012
• 卷：7478
• 期：1
• 页码：43-56
• 全文大小：870KB
• 参考文献：1. Bhasker, J., Sahni, S.: A linear algorithm to check for the existence of a rectangular dual of a planar triangulated graph. Networks聽7, 307鈥?17 (1987) CrossRef
  2. Buchin, K., Speckmann, B., Verdonschot, S.: Optimizing Regular Edge Labelings. In: Brandes, U., Cornelsen, S. (eds.) GD 2010. LNCS, vol.聽6502, pp. 117鈥?28. Springer, Heidelberg (2011) CrossRef
  3. Dent, B.D.: Cartography - thematic map design, 5th edn. McGraw-Hill (1999)
  4. Dorling, D.: Area Cartograms: their Use and Creation. Concepts and Techniques in Modern Geography, vol.聽59. University of East Anglia, Environmental Publications, Norwich (1996)
  5. Dougenik, J.A., Chrisman, N.R., Niemeyer, D.R.: An algorithm to construct continous area cartograms. Professional Geographer聽3, 75鈥?1 (1985) CrossRef
  6. Fusy, 脡.: Combinatoire des cartes planaires et applications algorithmiques. PhD thesis, 脡cole Polytechnique (2007)
  7. Fusy, 脡.: Transversal structures on triangulations: A combinatorial study and straight-line drawings. Disc. Math.聽309(7), 1870鈥?894 (2009) CrossRef
  8. Gastner, M., Newman, M.: Diffusion-based method for producing density-equalizing maps. Proceedings of the National Academy of Sciences of the United States of America (PNAS)聽101(20), 7499鈥?504 (2004) CrossRef
  9. Heilmann, R., Keim, D.A., Panse, C., Sips, M.: Recmap: Rectangular map approximations. In: Proceedings of the IEEE Symposium on Information Visualization (INFOVIS), pp. 33鈥?0 (2004)
  10. Inoue, R., Kitaura, K., Shimizu, E.: New solution for construction of rectilinear area cartogram. In: Proceedings of 24th International Cartography Conference. CD-ROM (2009)
  11. Kant, G., He, X.: Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems. Theoretical Computer Science聽172(1-2), 175鈥?93 (1997) CrossRef
  12. Ko藕mi艅ski, K., Kinnen, E.: Rectangular dual of planar graphs. Networks聽5, 145鈥?57 (1985)
  13. NCGIA/USGS. Cartogram Central (2002), http://www.ncgia.ucsb.edu/projects/Cartogram_Central/index.html
  14. Olson, J.: Noncontiguous area cartograms. Professional Geographer聽28, 371鈥?80 (1976) CrossRef
  15. Raisz, E.: The rectangular statistical cartogram. Geographical Review聽24, 292鈥?96 (1934) CrossRef
  16. Speckmann, B., van Kreveld, M., Florisson, S.: A linear programming approach to rectangular cartograms. In: Progress in Spatial Data Handling: Proc. 12th International Symposium on Spatial Data Handling, pp. 529鈥?46. Springer (2006)
  17. Tobler, W.: Pseudo-cartograms. The American Cartographer聽13, 43鈥?0 (1986) CrossRef
  18. van Kreveld, M., Speckmann, B.: On rectangular cartograms. Computational Geometry: Theory and Applications聽37(3), 175鈥?87 (2007) CrossRef
  
• 作者单位：Kevin Buchin (20)
  Bettina Speckmann (20)
  Sander Verdonschot (21)
  
  20. Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands
  21. School of Computer Science, Carleton University, Ottawa, Canada
  

文摘

A rectangular cartogram is a type of map where every region is a rectangle. The size of the rectangles is chosen such that their areas represent a geographic variable such as population or GDP. In recent years several algorithms for the automated construction of rectangular cartograms have been proposed, some of which are based on rectangular duals of the dual graph of the input map. In this paper we present a new approach to efficiently search within the exponentially large space of all possible rectangular duals. We employ evolution strategies that find rectangular duals which can be used for rectangular cartograms with correct adjacencies and (close to) zero cartographic error. This is a considerable improvement upon previous methods that have to either relax adjacency requirements or deal with larger errors. We present extensive experimental results for a large variety of data sets.