### 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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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 421-432 |

Number of pages | 12 |

Volume | 8125 LNCS |

DOIs | |

State | Published - 2013 |

Event | 21st Annual European Symposium on Algorithms, ESA 2013 - Sophia Antipolis, France Duration: Sep 2 2013 → Sep 4 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8125 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 21st Annual European Symposium on Algorithms, ESA 2013 |
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Country | France |

City | Sophia Antipolis |

Period | 9/2/13 → 9/4/13 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 8125 LNCS, pp. 421-432). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8125 LNCS). https://doi.org/10.1007/978-3-642-40450-4_36

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 8125 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8125 LNCS, pp. 421-432, 21st Annual European Symposium on Algorithms, ESA 2013, Sophia Antipolis, France, 9/2/13. https://doi.org/10.1007/978-3-642-40450-4_36

}

TY - GEN

T1 - Table cartograms

AU - Evans, William

AU - Felsner, Stefan

AU - Kaufmann, Michael

AU - Kobourov, Stephen G

AU - Mondal, Debajyoti

AU - Nishat, Rahnuma Islam

AU - Verbeek, Kevin

PY - 2013

Y1 - 2013

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.

UR - http://www.scopus.com/inward/record.url?scp=84884298955&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884298955&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-40450-4_36

DO - 10.1007/978-3-642-40450-4_36

M3 - Conference contribution

AN - SCOPUS:84884298955

SN - 9783642404498

VL - 8125 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 421

EP - 432

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -