Abstract
We consider the standard algorithm to test the upward planarity of embedded digraphs by Bertolazzi et al.[3]. We show how to improve its running time from O(n + r 2) to \(O(n+r^{\frac{3}{2}})\), where r is the number of sources and sinks in the digraph. We also discuss 2 applications of this technique: finding a certificate of correctness of an implementation of our upward planarity testing algorithm; and improving the running time of getting a quasi-upward planar drawing for an embedded digraph with minimum number of bends.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Di Battista, G., Tamassia, R.: Algorithms for plane representations of acyclic digraphs. Theor. Comput. Sci. 61, 175–198 (1988)
Bertolazzi, P., Di Battista, G., Didimo, W.: Quasi-upward planarity. Algorithmica 32(3), 474–506 (2002)
Bertolazzi, P., Di Battista, G., Liotta, G., Mannino, C.: Upward drawings of triconnected digraphs. Algorithmica 12(6), 476–497 (1994)
Bertolazzi, P., Di Battista, G., Mannino, C., Tamassia, R.: Optimal upward planarity testing of single-source digraphs. SIAM J. Comput. 27(1), 132–169 (1998)
Chan, H.: A parameterized algorithm for upward planarity testing. In: Proceedings of ESA, pp. 157–168 (2004)
Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, Englewood Cliffs (1999)
Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)
Healy, P., Lynch, K.: Fixed-parameter tractable algorithms for testing upward planarity. In: Proceedings of SOFSEM, pp. 199–208 (2005)
Hutton, M.D., Lubiw, A.: Upward planar drawing of single-source acyclic digraphs. SIAM J. Comput. 25(2), 291–311 (1996)
Kelly, D.: Fundamentals of planar ordered sets. Discrete Math 63(2-3), 197–216 (1987)
Mehlhorn, K.: Graph algorithms and NP-completeness. Springer, New York (1984)
Mehlhorn, K., Näher, S.: LEDA: a platform for combinatorial and geometric computing. Cambridge University Press, New York (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abbasi, S., Healy, P., Rextin, A. (2009). An Improved Upward Planarity Testing Algorithm and Related Applications. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-00202-1_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00201-4
Online ISBN: 978-3-642-00202-1
eBook Packages: Computer ScienceComputer Science (R0)