Advertisement

Adjacency-Preserving Spatial Treemaps

  • Kevin Buchin
  • David Eppstein
  • Maarten Löffler
  • Martin Nöllenburg
  • Rodrigo I. Silveira
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)

Abstract

Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political regions. A spatial treemap is a rectangular layout with a hierarchical structure: the outer rectangle is subdivided into rectangles that are in turn subdivided into smaller rectangles. We describe algorithms for transforming a rectangular layout that does not have this hierarchical structure, together with a clustering of the rectangles of the layout, into a spatial treemap that respects the clustering and also respects to the extent possible the adjacencies of the input layout.

Keywords

Planar Graph Global Region Dual Graph Bottom Level Outer Face 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice Hall, Englewood Cliffs (1993)zbMATHGoogle Scholar
  2. 2.
    Birkhoff, G.: Rings of sets. Duke Mathematical Journal 3(3), 443–454 (1937)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Buchin, K., Eppstein, D., Löffler, M., Nöllenburg, M., Silveira, R.I.: Adjacency-preserving spatial treemaps. Arxiv report, arXiv:1105.0398 (cs.CG) (May 2011)Google Scholar
  4. 4.
    Buchin, K., Speckmann, B., Verdonschot, S.: Optimizing regular edge labelings. In: Brandes, U., Cornelsen, S. (eds.) GD 2010. LNCS, vol. 6502, pp. 117–128. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Eppstein, D., Mumford, E.: Orientation-constrained rectangular layouts. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 266–277. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Eppstein, D., Mumford, E., Speckmann, B., Verbeek, K.: Area-universal rectangular layouts. In: Proc. SoCG, pp. 267–276 (2009)Google Scholar
  7. 7.
    Fusy, É.: Transversal structures on triangulations: A combinatorial study and straight-line drawings. Discrete Mathematics 309(8), 1870–1894 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Heilmann, R., Keim, D.A., Panse, C., Sips, M.: Recmap: Rectangular map approximations. In: Proceedings of the IEEE Symposium on Information Visualization, pp. 33–40. IEEE Computer Society, Washington, DC, USA (2004)CrossRefGoogle Scholar
  9. 9.
    Kant, G., He, X.: Two algorithms for finding rectangular duals of planar graphs. In: van Leeuwen, J. (ed.) WG 1993. LNCS, vol. 790, pp. 396–410. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  10. 10.
    Kant, G., He, X.: Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems. Theoretical Computer Science 172(1-2), 175–193 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kozminski, K., Kinnen, E.: Rectangular duals of planar graphs. Networks 5(2) (1985)Google Scholar
  12. 12.
    Mansmann, F., Keim, D.A., North, S.C., Rexroad, B., Sheleheda, D.: Visual analysis of network traffic for resource planning, interactive monitoring, and interpretation of security threats. IEEE Transactions on Visualization and Computer Graphics 13, 1105–1112 (2007)CrossRefGoogle Scholar
  13. 13.
    Raisz, E.: The rectangular statistical cartogram. Geographical Review 24(2), 292–296 (1934)CrossRefGoogle Scholar
  14. 14.
    Shneiderman, B.: Tree visualization with tree-maps: 2-d space-filling approach. ACM Trans. Graph. 11(1), 92–99 (1992)CrossRefzbMATHGoogle Scholar
  15. 15.
    Slingsby, A., Dykes, J., Wood, J.: Configuring hierarchical layouts to address research questions. IEEE Trans. Vis. Comput. Graph. 15(6), 977–984 (2009)CrossRefGoogle Scholar
  16. 16.
    Slingsby, A., Dykes, J., Wood, J.: Rectangular hierarchical cartograms for socio-economic data. Journal of Maps v2010, 330–345 (2010), doi:10.4113/jom.2010.1090CrossRefGoogle Scholar
  17. 17.
    van Kreveld, M., Speckmann, B.: On rectangular cartograms. CGTA 37(3) (2007)Google Scholar
  18. 18.
    Wood, J., Dykes, J.: Spatially ordered treemaps. IEEE Trans. Vis. Comput. Graph. 14(6), 1348–1355 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kevin Buchin
    • 1
  • David Eppstein
    • 2
  • Maarten Löffler
    • 2
  • Martin Nöllenburg
    • 3
  • Rodrigo I. Silveira
    • 4
  1. 1.Dept. of Mathematics and Computer ScienceTUEindhoven
  2. 2.Dept. of Computer ScienceUniversity of CaliforniaIrvine
  3. 3.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyGermany
  4. 4.Dept. de Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaSpain

Personalised recommendations