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Adjacency-Preserving Spatial Treemaps

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Algorithms and Data Structures (WADS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6844))

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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.

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References

  1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice Hall, Englewood Cliffs (1993)

    MATH  Google Scholar 

  2. Birkhoff, G.: Rings of sets. Duke Mathematical Journal 3(3), 443–454 (1937)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  6. Eppstein, D., Mumford, E., Speckmann, B., Verbeek, K.: Area-universal rectangular layouts. In: Proc. SoCG, pp. 267–276 (2009)

    Google Scholar 

  7. Fusy, É.: Transversal structures on triangulations: A combinatorial study and straight-line drawings. Discrete Mathematics 309(8), 1870–1894 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kozminski, K., Kinnen, E.: Rectangular duals of planar graphs. Networks 5(2) (1985)

    Google Scholar 

  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)

    Article  Google Scholar 

  13. Raisz, E.: The rectangular statistical cartogram. Geographical Review 24(2), 292–296 (1934)

    Article  Google Scholar 

  14. Shneiderman, B.: Tree visualization with tree-maps: 2-d space-filling approach. ACM Trans. Graph. 11(1), 92–99 (1992)

    Article  MATH  Google Scholar 

  15. Slingsby, A., Dykes, J., Wood, J.: Configuring hierarchical layouts to address research questions. IEEE Trans. Vis. Comput. Graph. 15(6), 977–984 (2009)

    Article  Google Scholar 

  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.2010.1090

    Article  Google Scholar 

  17. van Kreveld, M., Speckmann, B.: On rectangular cartograms. CGTA 37(3) (2007)

    Google Scholar 

  18. Wood, J., Dykes, J.: Spatially ordered treemaps. IEEE Trans. Vis. Comput. Graph. 14(6), 1348–1355 (2008)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Mathematics and Computer Science, TU, Eindhoven

    Kevin Buchin

  2. Dept. of Computer Science, University of California, Irvine

    David Eppstein & Maarten Löffler

  3. Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany

    Martin Nöllenburg

  4. Dept. de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Spain

    Rodrigo I. Silveira

Authors
  1. Kevin Buchin
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  2. David Eppstein
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  3. Maarten Löffler
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  4. Martin Nöllenburg
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  5. Rodrigo I. Silveira
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science and Engineering, Polytechnic Institute of New York University, 5 MetroTech Center, 11201, New York, NY, USA

    John Iacono

  3. School of Computer Science, Herzberg Laboratories, Carleton University, Herzberg Building, Room 5350, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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© 2011 Springer-Verlag Berlin Heidelberg

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Buchin, K., Eppstein, D., Löffler, M., Nöllenburg, M., Silveira, R.I. (2011). Adjacency-Preserving Spatial Treemaps. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_14

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  • DOI: https://doi.org/10.1007/978-3-642-22300-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22299-3

  • Online ISBN: 978-3-642-22300-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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