Pixel and Voxel Representations of Graphs

Alam, Muhammed Jawaherul and Bläsius, Thomas and Rutter, Ignaz and Ueckerdt, Torsten and Wolff, Alexander (2015) Pixel and Voxel Representations of Graphs. In: Graph Drawing and Network Visualization: 23rd International Symposium, GD 2015, September 24-26, 2015, Los Angeles, CA, USA , pp. 472-486 (Official URL: http://dx.doi.org/10.1007/978-3-319-27261-0_39).

Full text not available from this repository.

Item Type:Conference Paper
Classifications:G Algorithms and Complexity > G.560 Geometry
P Styles > P.060 3D
P Styles > P.999 Others
Z Theory > Z.500 Representations
ID Code:1513

Repository Staff Only: item control page


Aerts, N., Felsner, S.: Vertex contact graphs of paths on a grid. In: Kratsch, D., Todinca, I. (eds.) WG 2014. LNCS, vol. 8747, pp. 56–68. Springer, Heidelberg (2014)

Alam, M.J., Biedl, T., Felsner, S., Kaufmann, M., Kobourov, S., Ueckerdt, T.: Computing cartograms with optimal complexity. Discrete Comput. Geom. 50(3), 784–810 (2013)

Alam, M.J., Bläsius, T., Rutter, I., Ueckerdt, T., Wolff, A.: Pixel and voxel representations of graphs. Arxiv report (2015). arxiv.​org/​abs/​1507.​01450

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

Bezdek, A.: On the number of mutually touching cylinders. Comb. Comput. Geom. 52, 121–127 (2005)

Bezdek, K., Reid, S.: Contact graphs of unit sphere packings revisited. J. Geom. 104(1), 57–83 (2013)

Bhatt, S.N., Cosmadakis, S.S.: The complexity of minimizing wire lengths in VLSI layouts. Inform. Process. Lett. 25(4), 263–267 (1987)

Biedl, T.: On triangulating kk-outerplanar graphs. Discrete Appl. Math. 181, 275–279 (2015). arxiv.​org/​abs/​1310.​1845

Biedl, T.C.: Small drawings of outerplanar graphs, series-parallel graphs, and other planar graphs. Discrete Comput. Geom. 45(1), 141–160 (2011)

Bodlaender, H.L.: Treewidth: algorithmic techniques and results. In: Prívara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295, pp. 19–36. Springer, Heidelberg (1997)

Bose, P., Everett, H., Fekete, S.P., Houle, M.E., Lubiw, A., Meijer, H., Romanik, K., Rote, G., Shermer, T.C., Whitesides, S., Zelle, C.: A visibility representation for graphs in three dimensions. J. Graph Algorithms Appl. 2(3), 1–16 (1998)

Brandenburg, F.J., Eppstein, D., Goodrich, M.T., Kobourov, S.G., Liotta, G., Mutzel, P.: Selected open problems in graph drawing. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 515–539. Springer, Heidelberg (2004)

Brandenburg, F.J.: 1-visibility representations of 1-planar graphs. J. Graph Algorithms Appl. 18(3), 421–438 (2014)

Bremner, D., et al.: On representing graphs by touching cuboids. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 187–198. Springer, Heidelberg (2013)

Buchsbaum, A.L., Gansner, E.R., Procopiuc, C.M., Venkatasubramanian, S.: Rectangular layouts and contact graphs. ACM Trans. Algorithms 4(1), 8–28 (2008)

Cano, R., Buchin, K., Castermans, T., Pieterse, A., Sonke, W., Speckmann, B.: Mosaic drawings and cartograms. Comput. Graph. Forum 34(3), 361–370 (2015)

Chan, T.M., Goodrich, M.T., Kosaraju, S.R., Tamassia, R.: Optimizing area and aspect ratio in straight-line orthogonal tree drawings. Comput. Geom. Theory Appl. 23(2), 153–162 (2002)

Chaplick, S., Kobourov, S.G., Ueckerdt, T.: Equilateral L-contact graphs. In: Brandstädt, A., Jansen, K., Reischuk, R. (eds.) WG 2013. LNCS, vol. 8165, pp. 139–151. Springer, Heidelberg (2013)

Di Battista, G., Frati, F.: Small area drawings of outerplanar graphs. Algorithmica 54(1), 25–53 (2009)

Dolev, D., Leighton, T., Trickey, H.: Planar embedding of planar graphs. Adv. Comput. Res. 2, 147–161 (1984)

Dujmović, V., Morin, P., Wood, D.: Layered separators for queue layouts, 3d graph drawing and nonrepetitive coloring. In: Foundations of Computer Science (FOCS 2013), pp. 280–289. IEEE (2013)

Duncan, C.A., Gansner, E.R., Hu, Y.F., Kaufmann, M., Kobourov, S.G.: Optimal polygonal representation of planar graphs. Algorithmica 63(3), 672–691 (2012)

Evans, W., Kaufmann, M., Lenhart, W., Mchedlidze, T., Wismath, S.: Bar 1-visibility graphs and their relation to other nearly planar graphs. J. Graph Algorithms Appl. 18(5), 721–739 (2014)

Fan, J.-H., Lin, C.-C., Lu, H.-I., Yen, H.-C.: Width-optimal visibility representations of plane graphs. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 160–171. Springer, Heidelberg (2007)

Felsner, S.: Rectangle and square representations of planar graphs. Thirty Essays on Geometric Graph Theory, pp. 213–248 (2013)

Felsner, S., Francis, M.C.: Contact representations of planar graphs with cubes. In: Symposium on Computational Geometry (SoCG 2011), pp. 315–320. ACM (2011)

Fomin, F.V., Thilikos, D.M.: New upper bounds on the decomposability of planar graphs. J. Graph Theory 51(1), 53–81 (2006)

de Fraysseix, H., de Mendez, P.O.: Representations by contact and intersection of segments. Algorithmica 47(4), 453–463 (2007)

de Fraysseix, H., de Mendez, P.O., Rosenstiehl, P.: On triangle contact graphs. Comb. Prob. Comput. 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)

Hliněný, P., Kratochvíl, J.: Representing graphs by disks and balls (a survey of recognition-complexity results). Discrete Math. 229(1–3), 101–124 (2001)

Koebe, P.: Kontaktprobleme der konformen Abbildung. Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Math. Phy. Kla. 88, 141–164 (1936)

Leiserson, C.E.: Area-efficient graph layouts (for VLSI). In: Foundations of Computer Science (FOCS 1980), pp. 270–281. IEEE (1980)

Pach, J., Thiele, T., Tóth, G.: Three-dimensional grid drawings of graphs. In: Di Battista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 47–51. Springer, Heidelberg (1997)

Patrignani, M.: Complexity results for three-dimensional orthogonal graph drawing. J. Discrete Algorithms 6(1), 140–161 (2008)

Schnyder, W.: Embedding planar graphs on the grid. In: Symposium on Discrete Algorithms (SODA 1990), pp. 138–148. ACM-SIAM (1990)

Tamassia, R., Tollis, I.G.: A unified approach a visibility representation of planar graphs. Discrete Comput. Geom. 1, 321–341 (1986)

Thomassen, C.: Interval representations of planar graphs. J. Comb. Theory B 40(1), 9–20 (1986)

Zong, C.: The kissing numbers of tetrahedra. Discrete Comput. Geom. 15(3), 239–252 (1996)