# Table cartogram

W. Evans, S. Felsner, M. Kaufmann, S.G. Kobourov, D. Mondal, R.I. Nishat, K.A.B. Verbeek

2 Citations (Scopus)

### 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.

Original language English 174-185 12 Computational Geometry 68 https://doi.org/10.1016/j.comgeo.2017.06.010 Published - 2018

Table
Rectangle
Cell
Partition
Face
Circle
Non-negative
Generalise
Arbitrary

### Keywords

• Cartogram
• Data visualization
• Grid map
• Tree map

### Cite this

Evans, W., Felsner, S., Kaufmann, M., Kobourov, S. G., Mondal, D., Nishat, R. I., & Verbeek, K. A. B. (2018). Table cartogram. Computational Geometry, 68, 174-185. https://doi.org/10.1016/j.comgeo.2017.06.010
Evans, W. ; Felsner, S. ; Kaufmann, M. ; Kobourov, S.G. ; Mondal, D. ; Nishat, R.I. ; Verbeek, K.A.B. / Table cartogram. In: Computational Geometry. 2018 ; Vol. 68. pp. 174-185.
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Evans, W, Felsner, S, Kaufmann, M, Kobourov, SG, Mondal, D, Nishat, RI & Verbeek, KAB 2018, 'Table cartogram', Computational Geometry, vol. 68, pp. 174-185. https://doi.org/10.1016/j.comgeo.2017.06.010

Table cartogram. / Evans, W.; Felsner, S.; Kaufmann, M.; Kobourov, S.G.; Mondal, D.; Nishat, R.I.; Verbeek, K.A.B.

In: Computational Geometry, Vol. 68, 2018, p. 174-185.

TY - JOUR

T1 - Table cartogram

AU - Evans, W.

AU - Felsner, S.

AU - Kaufmann, M.

AU - Kobourov, S.G.

AU - Mondal, D.

AU - Nishat, R.I.

AU - Verbeek, K.A.B.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Cartogram

KW - Data visualization

KW - Grid map

KW - Tree map

UR - http://www.scopus.com/inward/record.url?scp=85021883604&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2017.06.010

DO - 10.1016/j.comgeo.2017.06.010

M3 - Article

AN - SCOPUS:85021883604

VL - 68

SP - 174

EP - 185

JO - Computational Geometry

JF - Computational Geometry

SN - 0925-7721

ER -

Evans W, Felsner S, Kaufmann M, Kobourov SG, Mondal D, Nishat RI et al. Table cartogram. Computational Geometry. 2018;68:174-185. https://doi.org/10.1016/j.comgeo.2017.06.010