### 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 (US) |
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Journal | Computational Geometry: Theory and Applications |

DOIs | |

State | Accepted/In press - 2017 |

### Fingerprint

### Keywords

- Cartogram
- Data visualization
- Grid map
- Tree map

### ASJC Scopus subject areas

- Geometry and Topology
- Computer Science Applications
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computational Geometry: Theory and Applications*. https://doi.org/10.1016/j.comgeo.2017.06.010

**Table cartogram.** / Evans, William; Felsner, Stefan; Kaufmann, Michael; Kobourov, Stephen G; Mondal, Debajyoti; Nishat, Rahnuma Islam; Verbeek, Kevin.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*. https://doi.org/10.1016/j.comgeo.2017.06.010

}

TY - JOUR

T1 - Table cartogram

AU - Evans, William

AU - Felsner, Stefan

AU - Kaufmann, Michael

AU - Kobourov, Stephen G

AU - Mondal, Debajyoti

AU - Nishat, Rahnuma Islam

AU - Verbeek, Kevin

PY - 2017

Y1 - 2017

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

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

U2 - 10.1016/j.comgeo.2017.06.010

DO - 10.1016/j.comgeo.2017.06.010

M3 - Article

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

ER -