Abstract
A straight-line drawing of a graph is an open weak rectangle-of-influence (RI) drawing, if there is no vertex in the relative interior of the axis-parallel rectangle induced by the end points of each edge. No algorithm is known to test whether a graph has a planar open weak RI-drawing, not even for inner triangulated graphs.
In this paper, we study RI-drawings that must have a non-aligned frame, i.e., the graph obtained from removing the interior of every filled triangle is drawn such that no two vertices have the same coordinate. We give a polynomial algorithm to test whether an inner triangulated graph has a planar open weak RI-drawing with non-aligned frame.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alamdari, S., Biedl, T.: Planar Open Rectangle-of-Influence Drawings with Non-Aligned Frames. Technical Report CS-2011-17, David R. Cheriton School of Computer Science, University of Waterloo (2011)
Battista, G.D., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall (1998)
Biedl, T.C., Bretscher, A., Meijer, H.: Rectangle of Influence Drawings of Graphs without Filled 3-Cycles. In: KratochvÃl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 359–368. Springer, Heidelberg (1999)
Fusy, E.: Transversal structures on triangulations: A combinatorial study and straight-line drawings. Discrete Mathematics 309(7), 1870–1894 (2009)
Goldberg, A.V., Rao, S.: Beyond the flow decomposition barrier. J. ACM 45, 783–797 (1998)
Kozminski, K., Kinnen, E.: Rectangular dual of planar graphs. Networks 5, 145–157 (1985)
Leinwand, S.M., Lai, Y.-T.: An algorithm for building rectangular floor-plans. In: 21st Design Automation Conference, pp. 663–664. IEEE Press (1984)
Liotta, G., Lubiw, A., Meijer, H., Whitesides, S.H.: The rectangle of influence drawability problem. Computational Geometry 10(1), 1–22 (1998)
Miura, K., Haga, H., Nishizeki, T.: Inner rectangular drawings of plane graphs. Int. J. Comput. Geometry Appl. 16(2-3), 249–270 (2006)
Miura, K., Matsuno, T., Nishizeki, T.: Open rectangle-of-influence drawings of inner triangulated plane graphs. Discrete & Computational Geometry 41(4), 643–670 (2009)
Miura, K., Nishizeki, T.: Rectangle-of-influence drawings of four-connected plane graphs. In: Asia-Pacific Symposium on Information Visualization (APVIS). CRPIT, vol. 45, pp. 75–80 (2005)
Sadasivam, S., Zhang, H.: Closed rectangle-of-influence drawings for irreducible triangulations. Comput. Geom. Theory Appl. 44, 9–19 (2011)
Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput. 16, 421–444 (1987)
Ungar, P.: On diagrams representing maps. J. London Mathematical Society 28(3), 336–342 (1953)
Zhang, H., Vaidya, M.: On open rectangle-of-influence and rectangular dual drawings of plane graphs. Discrete Mathematics, Algorithms and Applications 1, 319–333 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alamdari, S., Biedl, T. (2012). Planar Open Rectangle-of-Influence Drawings with Non-aligned Frames. In: van Kreveld, M., Speckmann, B. (eds) Graph Drawing. GD 2011. Lecture Notes in Computer Science, vol 7034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25878-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-25878-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25877-0
Online ISBN: 978-3-642-25878-7
eBook Packages: Computer ScienceComputer Science (R0)