Abstract
In this paper we introduce cyclic level planar graphs, which are a planar version of the recurrent hierarchies from Sugiyama et al. [8] and the cyclic extension of level planar graphs, where the first level is the successor of the last level. We study the testing and embedding problem and solve it for strongly connected graphs in time \(\O(|V| \log |V|)\).
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
Bachmaier, C., Brandenburg, F.J., Forster, M.: Radial level planarity testing and embedding in linear time. Journal of Graph Algorithms and Applications 9(1), 53–97 (2005)
Boyer, J., Myrvold, W.: On the cutting edge: Simplified \(\mathcal{O}(n)\) planarity by edge addition. Journal of Graph Algorithms and Applications 8(3), 241–273 (2004)
de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)
Healy, P., Kuusik, A.: Algorithms for multi-level graph planarity testing and layout. Theoretical Computer Science 320(2–3), 331–344 (2004)
Hopcroft, J.E., Tarjan, R.E.: Efficient planarity testing. Journal of the ACM 21(4), 549–568 (1974)
Jünger, M., Leipert, S.: Level planar embedding in linear time. Journal of Graph Algorithms and Applications 6(1), 67–113 (2002)
Kaufmann, M., Wagner, D.: Drawing Graphs. LNCS, vol. 2025. Springer, Heidelberg (2001)
Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE Transactions on Systems, Man, and Cybernetics 11(2), 109–125 (1981)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bachmaier, C., Brunner, W., König, C. (2008). Cyclic Level Planarity Testing and Embedding. In: Hong, SH., Nishizeki, T., Quan, W. (eds) Graph Drawing. GD 2007. Lecture Notes in Computer Science, vol 4875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77537-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-77537-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77536-2
Online ISBN: 978-3-540-77537-9
eBook Packages: Computer ScienceComputer Science (R0)