Table cartograms

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

doi:10.1007/978-3-642-40450-4_36

Table cartograms

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

11 Citations (Scopus)

4 Downloads (Pure)

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
Title of host publication	Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings)
Editors	H.L. Bodlaender, G.F. Italiano
Place of Publication	Berlin
Publisher	Springer
Pages	421-432
ISBN (Print)	978-3-642-40449-8
DOIs	https://doi.org/10.1007/978-3-642-40450-4_36
Publication status	Published - 2013
Externally published	Yes
Event	21st Annual European Symposium on Algorithms (ESA 2013) - Sophia Antipolis, France Duration: 2 Sept 2013 → 4 Sept 2013 Conference number: 21st http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2013.html

Publication series

Name	Lecture Notes in Computer Science
Volume	8125
ISSN (Print)	0302-9743

Conference

Conference	21st Annual European Symposium on Algorithms (ESA 2013)
Abbreviated title	ESA 2013
Country/Territory	France
City	Sophia Antipolis
Period	2/09/13 → 4/09/13
Internet address	http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2013.html

Access to Document

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

Cite this

Evans, W. S., Felsner, S., Kaufmann, M., Kobourov, S. G., Mondal, D., Nishat, R. I., & Verbeek, K. A. B. (2013). Table cartograms. In H. L. Bodlaender, & G. F. Italiano (Eds.), Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings) (pp. 421-432). (Lecture Notes in Computer Science; Vol. 8125). Springer. https://doi.org/10.1007/978-3-642-40450-4_36

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title = "Table cartograms",

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{\textquoteright}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.",

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

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doi = "10.1007/978-3-642-40450-4\_36",

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editor = "H.L. Bodlaender and G.F. Italiano",

booktitle = "Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings)",

address = "Germany",

note = "21st Annual European Symposium on Algorithms (ESA 2013), ESA 2013 ; Conference date: 02-09-2013 Through 04-09-2013",

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}

Evans, WS, Felsner, S, Kaufmann, M, Kobourov, SG, Mondal, D, Nishat, RI & Verbeek, KAB 2013, Table cartograms. in HL Bodlaender & GF Italiano (eds), Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings). Lecture Notes in Computer Science, vol. 8125, Springer, Berlin, pp. 421-432, 21st Annual European Symposium on Algorithms (ESA 2013), Sophia Antipolis, France, 2/09/13. https://doi.org/10.1007/978-3-642-40450-4_36

Table cartograms. / Evans, W.S.; Felsner, S.; Kaufmann, M. et al.
Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings). ed. / H.L. Bodlaender; G.F. Italiano. Berlin: Springer, 2013. p. 421-432 (Lecture Notes in Computer Science; Vol. 8125).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Table cartograms

AU - Evans, W.S.

AU - Felsner, S.

AU - Kaufmann, M.

AU - Kobourov, S.G.

AU - Mondal, D.

AU - Nishat, R.I.

AU - Verbeek, K.A.B.

N1 - Conference code: 21st

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.

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

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

M3 - Conference contribution

SN - 978-3-642-40449-8

T3 - Lecture Notes in Computer Science

SP - 421

EP - 432

BT - Algorithms – ESA 2013 (21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings)

A2 - Bodlaender, H.L.

A2 - Italiano, G.F.

PB - Springer

CY - Berlin

T2 - 21st Annual European Symposium on Algorithms (ESA 2013)

Y2 - 2 September 2013 through 4 September 2013

ER -

Table cartograms

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