Proportional Contact Representations of Planar Graphs

Alam, Muhammed Jawaherul and Biedl, Therese and Felsner, Stefan and Kaufmann, Michael and Kobourov, Stephen G. (2012) Proportional Contact Representations of Planar Graphs. In: Graph Drawing 19th International Symposium, GD 2011, September 21-23, 2011, Eindhoven, The Netherlands , pp. 26-38 (Official URL:

Full text not available from this repository.


We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Several natural optimization goals for such representations include minimizing the complexity of the polygons, the cartographic error, and the unused area. We describe constructive algorithms for proportional contact representations with optimal complexity for general planar graphs and planar 2-segment graphs, which include maximal outerplanar graphs and partial 2-trees.

Item Type:Conference Paper
Additional Information:10.1007/978-3-642-25878-7_4
Classifications:M Methods > M.600 Planar
Z Theory > Z.500 Representations
ID Code:1238

Repository Staff Only: item control page


Alam, M.J., Biedl, T., Felsner, S., Gerasch, A., Kaufmann, M., Kobourov, S.G., Ueckert, T.: Computing cartograms with optimal complexity (submitted, 2011)

Alam, M.J., Biedl, T., Felsner, S., Kaufmann, M., Kobourov, S.G.: Proportional contact representations of planar graphs. Technical Report CS-2011-11. University of Waterloo (2011)

Badent, M., Binucci, C., Giacomo, E.D., Didimo, W., Felsner, S., Giordano, F., Kratochvíl, J., Palladino, P., Patrignani, M., Trotta, F.: Homothetic triangle contact representations of planar graphs. In: CCCG 2007, pp. 233–236 (2007)

Buchsbaum, A.L., Gansner, E.R., Procopiuc, C.M., Venkatasubramanian, S.: Rectangular layouts and contact graphs. ACM Transactions on Algorithms 4(1) (2008)

de Fraysseix, H., de Mendez, P.O., Rosenstiehl, P.: On triangle contact graphs. Combinatorics, Probability and Computing 3, 233–246 (1994)

de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)

Debrunner, H.: Aufgabe 260. Elemente der Mathematik 12 (1957)

Felsner, S., Francis, M.C.: Contact representations of planar graphs with cubes. In: Proc. ACM Symposium on Computational Geometry (2011)

Gansner, E.R., Hu, Y.F., Kaufmann, M., Kobourov, S.G.: Optimal Polygonal Representation of Planar Graphs. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 417–432. Springer, Heidelberg (2010)

Gansner, E.R., Hu, Y., Kobourov, S.G.: On Touching Triangle Graphs. In: Brandes, U.,Cornelsen, S. (eds.) GD 2010. LNCS, vol. 6502, pp. 250–261. Springer, Heidelberg (2011)

Gonçalves, D., Lévêque, B., Pinlou, A.: Triangle Contact Representations and Duality. In: Brandes, U., Cornelsen, S. (eds.) GD 2010. LNCS, vol. 6502, pp. 262–273. Springer, Heidelberg (2011)

Hartman, I., Newman, I., Ziv, R.: On grid intersection graphs. Discrete Mathematics 97, 41–52 (1991)

Heilmann, R., Keim, D.A., Panse, C., Sips, M.: Recmap: Rectangular map approximations. In: 10th IEEE Symp. on Information Visualization (InfoVis 2004), pp. 33–40 (2004)

Hliněný, P.: Contact graphs of line segments are NP-complete. Discr. Math. 235, 95–106 (2001)

Koebe, P.: Kontaktprobleme der konformen Abbildung. Berichte uber die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Math.-Phys. Kl. 88, 141–164 (1936)

Koźmiński, K., Kinnen, E.: Rectangular duals of planar graphs. Networks 15, 145–157 (1985)

Lee, A., Streinu, I.: Pebble game algorithms and sparse graphs. Discrete Mathematics 308(8), 1425–1437 (2008)

Schnyder, W.: Embedding planar graphs on the grid. In: SODA, pp. 138–148 (1990)

Ungar, P.: On diagrams representing graphs. J. London Math. Soc. 28, 336–342 (1953)

van Kreveld, M.J., Speckmann, B.: On rectangular cartograms. Computational Geometry 37(3), 175–187 (2007)

Yeap, K.-H., Sarrafzadeh, M.: Floor-planning by graph dualization: 2-concave rectilinear modules. SIAM Journal on Computing 22, 500–526 (1993)