Abstract
We study a new standard for visualizing graphs: A monotone drawing is a straight-line drawing such that, for every pair of vertices, there exists a path that monotonically increases with respect to some direction. We show algorithms for constructing monotone planar drawings of trees and biconnected planar graphs, we study the interplay between monotonicity, planarity, and convexity, and we outline a number of open problems and future research directions.
Supported in part by MIUR (Italy), Projects AlgoDEEP no. 2008TFBWL4 and FIRB “Advanced tracking system in intermodal freight transportation”, no. RBIP06BZW8.
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
Angelini, P., Colasante, E., di Battista, G., Frati, F., Patrignani, M.: Monotone drawings of graphs. Tech. Report 178, Dip. di Informatica e Automazione, Università Roma Tre (2010)
Angelini, P., Frati, F., Grilli, L.: An algorithm to construct greedy drawings of triangulations. J. Graph Alg. Appl. 14(1), 19–51 (2010)
Arkin, E.M., Connelly, R., Mitchell, J.S.: On monotone paths among obstacles with applications to planning assemblies. In: SoCG 1989, pp. 334–343 (1989)
Brocot, A.: Calcul des rouages par approximation, nouvelle methode. Revue Chronometrique 6, 186–194 (1860)
Carlson, J., Eppstein, D.: Trees with convex faces and optimal angles. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 77–88. Springer, Heidelberg (2007)
Chiba, N., Nishizeki, T.: Planar Graphs: Theory and Algorithms. In: Annals of Discrete Mathematics, vol. 32, North-Holland, Amsterdam (1988)
Di Battista, G., Tamassia, R.: Algorithms for plane representations of acyclic digraphs. Theor. Comput. Sci. 61, 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.: On-line planarity testing. SIAM J. Comp. 25(5), 956–997 (1996)
Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comp. 31(2), 601–625 (2001)
Gutwenger, C., Mutzel, P.: A linear time implementation of SPQR-trees. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 77–90. Springer, Heidelberg (2001)
Moitra, A., Leighton, T.: Some results on greedy embeddings in metric spaces. In: Foundations of Computer Science (FOCS 2008), pp. 337–346 (2008)
Papadimitriou, C.H., Ratajczak, D.: On a conjecture related to geometric routing. Theoretical Computer Science 344(1), 3–14 (2005)
Stern, M.A.: Ueber eine zahlentheoretische funktion. Journal fur die reine und angewandte Mathematik 55, 193–220 (1858)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Angelini, P., Colasante, E., Di Battista, G., Frati, F., Patrignani, M. (2011). Monotone Drawings of Graphs. In: Brandes, U., Cornelsen, S. (eds) Graph Drawing. GD 2010. Lecture Notes in Computer Science, vol 6502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18469-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-18469-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18468-0
Online ISBN: 978-3-642-18469-7
eBook Packages: Computer ScienceComputer Science (R0)