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European Symposium on Algorithms

ESA 2013: Algorithms – ESA 2013 pp 421–432Cite as

Table Cartograms

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8125)

Abstract

A table cartogram of a two dimensional m ×n table A of non-negative weights in a rectangle R, whose area equals the sum of the weights, is a partition of R into convex quadrilateral faces corresponding to the cells of A such that each face has the same adjacency as its corresponding cell and has area equal to the cell’s weight. Such a partition acts as a natural way to visualize table data arising in various fields of research. In this paper, we give a O(mn)-time algorithm to find a table cartogram in a rectangle. We then generalize our algorithm to obtain table cartograms inside arbitrary convex quadrangles, circles, and finally, on the surface of cylinders and spheres.

Keywords

  • Outerplanar Graph
  • Interesting Open Problem
  • Correct Area
  • Concave Corner
  • Convex Quadrilateral

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.

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  • DOI: 10.1007/978-3-642-40450-4_36
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Author information

Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, Canada

    William Evans

  2. Institut für Mathematik, Technische Universität Berlin, Germany

    Stefan Felsner

  3. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany

    Michael Kaufmann

  4. Department of Computer Science, University of Arizona, USA

    Stephen G. Kobourov

  5. Department of Computer Science, University of Manitoba, Canada

    Debajyoti Mondal

  6. Department of Computer Science, University of Victoria, Canada

    Rahnuma Islam Nishat

  7. Department of Computer Science, University of California, Santa Barbara, USA

    Kevin Verbeek

Authors
  1. William Evans
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  2. Stefan Felsner
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  3. Michael Kaufmann
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  4. Stephen G. Kobourov
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  5. Debajyoti Mondal
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  6. Rahnuma Islam Nishat
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  7. Kevin Verbeek
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Rome, Italy

    Giuseppe F. Italiano

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Evans, W. et al. (2013). Table Cartograms. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_36

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  • DOI: https://doi.org/10.1007/978-3-642-40450-4_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40449-8

  • Online ISBN: 978-3-642-40450-4

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