Abstract
A planar graph visibility representation maps each vertex to a horizontal segment at a vertical position and each edge to a vertical segment at a horizontal position such that each edge segment terminates at the vertical positions of its endpoint vertices and intersects no other horizontal vertex segments. The first O(n) algorithms for producing visibility representations were presented in [4, 5]. These were based on pre-processing to compute both an st-numbering and the dual of the planar graph, which were then used with the combinatorial planar embedding to produce a visibility representation. Greater efficiency is obtained in [3] by eliminating the need for the planar graph dual and by re-using the pre-computed st-numbering in the PQ-tree [1] algorithm.
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
Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ–tree algorithms. Journal of Computer and Systems Sciences 13, 335–379 (1976)
Boyer, J., Myrvold, W.: On the cutting edge: Simplified O(n) planarity by edge addition. Journal of Graph Algorithms and Applications 8(3), 241–273 (2004)
Jayakumar, R., Thulasiraman, K., Swamy, M.N.S.: Planar embedding: Linear-time algorithms for vertex placement and edge ordering. IEEE Transactions on Circuits and Systems 35(3), 334–344 (1988)
Rosenstiehl, P., Tarjan, R.: Rectilinear planar layouts and bipolar orientations of planar graphs. Discrete and Computational Geometry 1(4), 343–353 (1986)
Tamassia, R., Tollis, I.G.: A unified approach to visibility representations of planar graphs. Discrete and Computational Geometry 1(4), 321–341 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boyer, J.M. (2006). A New Method for Efficiently Generating Planar Graph Visibility Representations. In: Healy, P., Nikolov, N.S. (eds) Graph Drawing. GD 2005. Lecture Notes in Computer Science, vol 3843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11618058_47
Download citation
DOI: https://doi.org/10.1007/11618058_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31425-7
Online ISBN: 978-3-540-31667-1
eBook Packages: Computer ScienceComputer Science (R0)