Abstract
A monotone drawing of a graph G is a straight line drawing of G where a monotone path exists between every pair of vertices of G in some direction. Recently monotone drawings of graphs have been discovered as a new standard for visualizing graphs. In this paper we study monotone drawings of series-parallel graphs in a variable embedding setting. We show that a series-parallel graph of n vertices has a straight-line planar monotone drawing on a grid of size O(n)×O(n 2).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Angelini, P., Colasante, E., Di Battista, G., Frati, F., Patrignani, M.: Monotone drawings of graphs. Journal of Graph Algorithms and Applications 16(1), 5–35 (2012)
Angelini, P., Didimo, W., Kobourov, S., Mchedlidze, T., Roselli, V., Symvonis, A., Wismath, S.: Monotone drawings of graphs with fixed embedding. In: Speckmann, B. (ed.) GD 2011. LNCS, vol. 7034, pp. 379–390. Springer, Heidelberg (2011)
Arkin, E.M., Connelly, R., Mitchell, J.S.: On monotone paths among obstacles with applications to planning assemblies. In: Proceedings of the Fifth Annual Symposium on Computational Geometry, SCG 1989, pp. 334–343. ACM, New York (1989)
Di Battista, G., Tamassia, R.: Algorithms for plane representations of acyclic digraphs. Theoretical Computer Science 61(2-3), 175–198 (1988)
Di Battista, G., Tamassia, R.: On-line maintenance of triconnected components with spqr-trees. Algorithmica 15(4), 302–318 (1996)
Di Battista, G., Tamassia, R., Vismara, L.: Output-sensitive reporting of disjoint paths. Algorithmica 23, 302–340 (1999)
Rahman, M.S., Egi, N., Nishizeki, T.: No-bend orthogonal drawings of series-parallel graphs. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 409–420. Springer, Heidelberg (2006)
Samee, M.A.H., Rahman, M.S.: Upward planar drawings of series-parallel digraphs with maximum degree three. In: WALCOM 2007, pp. 28–45 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hossain, M.I., Rahman, M.S. (2013). Straight-Line Monotone Grid Drawings of Series-Parallel Graphs. In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_59
Download citation
DOI: https://doi.org/10.1007/978-3-642-38768-5_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38767-8
Online ISBN: 978-3-642-38768-5
eBook Packages: Computer ScienceComputer Science (R0)