Abstract
In this paper we present a novel approach for cluster-based drawing of large planar graphs that maintains planarity. Our technique works for arbitrary planar graphs and produces a clustering which satisfies the conditions for compound-planarity (c-planarity). Using the clustering, we obtain a representation of the graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. At the same time, the difference between two graphs on neighboring layers of the hierarchy is small, thus preserving the viewer’s mental map. The overall running time of the algorithm is O(n log n), where n is the number of vertices of graph G.
Partially supported by NSF grant CCR-9732300 and ARO grant DAAH04-96-1-0013.
Also at Max-Planck-Institut für Informatik.
Chapter PDF
Similar content being viewed by others
References
C. A. Duncan, M. T. Goodrich, and S. G. Kobourov. Balanced aspect ratio trees and their use for drawing very large graphs. Proc. of 6th Symposium on Graph Drawing (GD’98), LNCS 1190:101–112, 1998.
P. Eades and Q. W. Feng. Multilevel visualization of clustered graphs. Proc. of 4th Symposium on Graph Drawing (GD’96), LNCS 1190:101–112, 1996.
P. Eades, Q. W. Feng, and X. Lin. Straight-line drawing algorithms for hierarchical graphs and clustered graphs. Proc. of the 4th Symposium on Graph Drawing (GD’96), LNCS 1190:113–128, 1997.
I. Fary. On straight lines representation of planar graphs. Acta Sci. Math. Szeged, 11:229–233, 1948.
Q.-W. Feng, R. F. Cohen, and P. Eades. Planarity for clustered graphs. ESA’95, LNCS 979:213–226, 1995.
R. J. Lipton and R. E. Tarjan. A separator theorem for planar graphs. SIAM J. Appl. Math., 36:177–189, 1979.
F. J. Newbery. Edge concentration: A method for clustering directed graphs. In Proceedings of the 2nd International Workshop on Software Configuration Management, pages 76–85, Princeton, New Jersey, October 1989.
S. C. North. Drawing ranked digraphs with recursive clusters. ALCOM International Workshop PARIS 1993 on Graph Drawing and Topological Graph Algorithms (GD’93), September 1993.
Sablowski and Frick. Automatic graph clustering. Proc. of 4th Symposium on Graph Drawing (GD’96), LNCS 1190:395–400, 1996.
W. Schnyder. Embedding planar graphs on the grid. In Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pages 138–148, 1990.
K. Sugiyama and K. Misue. Visualization of structural information: Automatic drawing of compound digraphs. IEEE Trans. Softw. Eng., 21(4):876–892, 1991.
K. Wagner. Bemerkungen zum vierfarbenproblem. Jahresbericht der Deutschen Mathematiker-Vereinigung, 46:26–32, 1936.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Duncan, C.A., Goodrich, M.T., Kobourov, S.G. (1999). Planarity-Preserving Clustering and Embedding for Large Planar Graphs. In: KratochvÃyl, J. (eds) Graph Drawing. GD 1999. Lecture Notes in Computer Science, vol 1731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46648-7_19
Download citation
DOI: https://doi.org/10.1007/3-540-46648-7_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66904-3
Online ISBN: 978-3-540-46648-2
eBook Packages: Springer Book Archive