Abstract
Among various styles of tree drawing, balloon drawing, where each subtree is enclosed in a circle, enjoys a desirable feature of displaying tree structures in a rather balanced fashion. We first design an efficient algorithm to optimize angular resolution and aspect ratio for the balloon drawing of rooted unordered trees. For the case of ordered trees for which the center of the enclosing circle of a subtree need not coincide with the root of the subtree, flipping the drawing of a subtree (along the axis from the parent to the root of the subtree) might change both the aspect ratio and the angular resolution of the drawing. We show that optimizing the angular resolution as well as the aspect ratio with respect to this type of rooted ordered trees is reducible to the perfect matching problem for bipartite graphs, which is solvable in polynomial time. Aside from studying balloon drawing from an algorithmic viewpoint, we also propose a local magnetic spring model for producing dynamic balloon drawings with applications to the drawings of galaxy systems, H-trees, and sparse graphs, which are of practical interest.
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
Carrière, J., Kazman, R.: Reserch report: Interacting with huge hierarchies: Beyond cone trees. In: IV 1995, pp. 74–81. IEEE CS Press, Los Alamitos (1995)
Eades, P.: A heuristic for graph drawing. Congress Numerantium 42, 149–160 (1984)
Jeong, C.-S., Pang, A.: Reconfigurable disc trees for visualizing large hierarchical information space. In: InfoVis 1998, pp. 19–25. IEEE CS Press, Los Alamitos (1998)
Koike, H., Yoshihara, H.: Fractal approaches for visualizing huge hierarchies. In: VL 1993, pp. 55–60. IEEE CS Press, Los Alamitos (1993)
Lamping, J., Rao, R., Pirolli, P.: A focus+context technique based on hyperbolic geometry for visualizing large hierarchies. In: CHI 1995, pp. 401–408. ACM Press, New York (1995)
Melançon, G., Herman, I.: Circular drawing of rooted trees. Reports of the Centre for Mathematics and Computer Sciences. Report number INS-9817 (1998), available at: http://www.cwi.nl/InfoVis/papers/circular.pdf
Papadimitriou, C.H., Steiglitz, K.: Combinatorial optimization. Prentice Hall, Englewood Cliffs (1982)
Reingold, E., Tilford, J.: Tidier drawing of trees. IEEE Trans. Software Eng. SE-7(2), 223–228 (1981)
Robertson, G., Mackinlay, J., Card, S.: Cone trees: Animated 3d visualizations of hierarchical information, human factors in computing systems. In: CHI 1991, pp. 189–194. ACM Press, New York (1991)
Shiloach, Y.: Arrangements of planar graphs on the planar lattices. Ph D Thesis, Weizmann Instite of Science, Rehovot, Israel (1976)
Sugiyama, K., Misue, K.: Graph drawing by the magnetic spring model. J. Vis. Lang. Comput. 6, 217–231 (1995)
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
Lin, CC., Yen, HC. (2006). On Balloon Drawings of Rooted Trees. 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_26
Download citation
DOI: https://doi.org/10.1007/11618058_26
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)