Monotone Drawings of Graphs

  • Patrizio Angelini
  • Enrico Colasante
  • Giuseppe Di Battista
  • Fabrizio Frati
  • Maurizio Patrignani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6502)


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.


Planar Graph Outer Face Inductive Algorithm Planar Drawing Virtual Edge 
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.


  1. 1.
    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)Google Scholar
  2. 2.
    Angelini, P., Frati, F., Grilli, L.: An algorithm to construct greedy drawings of triangulations. J. Graph Alg. Appl. 14(1), 19–51 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    Brocot, A.: Calcul des rouages par approximation, nouvelle methode. Revue Chronometrique 6, 186–194 (1860)Google Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Chiba, N., Nishizeki, T.: Planar Graphs: Theory and Algorithms. In: Annals of Discrete Mathematics, vol. 32, North-Holland, Amsterdam (1988)Google Scholar
  7. 7.
    Di Battista, G., Tamassia, R.: Algorithms for plane representations of acyclic digraphs. Theor. Comput. Sci. 61, 175–198 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Di Battista, G., Tamassia, R.: On-line maintenance of triconnected components with SPQR-trees. Algorithmica 15(4), 302–318 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Di Battista, G., Tamassia, R.: On-line planarity testing. SIAM J. Comp. 25(5), 956–997 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comp. 31(2), 601–625 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Moitra, A., Leighton, T.: Some results on greedy embeddings in metric spaces. In: Foundations of Computer Science (FOCS 2008), pp. 337–346 (2008)Google Scholar
  13. 13.
    Papadimitriou, C.H., Ratajczak, D.: On a conjecture related to geometric routing. Theoretical Computer Science 344(1), 3–14 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Stern, M.A.: Ueber eine zahlentheoretische funktion. Journal fur die reine und angewandte Mathematik 55, 193–220 (1858)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Enrico Colasante
    • 1
  • Giuseppe Di Battista
    • 1
  • Fabrizio Frati
    • 1
  • Maurizio Patrignani
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreItaly

Personalised recommendations