Abstract
Hierarchical graphs and clustered graphs are useful nonclassical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualization, VLSI design, etc. Drawing algorithms for hierarchical graphs have been well investigated. However, the problem of straight-line representation has not been addressed. In this paper, we answer the question: does every planar hierarchical graph admit a planar straight-line hierarchical drawing? We present an algorithm that constructs such drawings in O(n 2) time. Also, we answer a basic question for clustered graphs, i.e. does every planar clustered graph admit a planar straight-line drawing with clusters drawn as convex polygons? A method for such drawings is provided in this paper.
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
G. Di Battista and R. Tamassia. Algorithms for plane representations of acyclic digraphs. Theoretical Computer Science, 61:175–198, 1988.
J.A. Bondy and U.S.R. Murty. Graph Theory with Applications. North-Holland, New York, N.Y., 1976.
P. Eades and K. Sugiyama. How to draw a directed graph. Journal of Information Processing, 424–437, 1991.
Peter Eades and Qing-Wen Feng. Orthogonal grid drawing of clustered graphs. Technical Report 96-04, Department of Computer Science, The University of Newcastle, Australia, 1996.
Peter D. Eades, Xuemin Lin, and Roberto Tamassia. An algorithm for drawing a hierarchical graph. International Journal of Computational Geometry and Applications, 1995.
S. Even and R. E. Tarjan. Computing an st-numbering. Theoretical Computer Science, 2:339–344, 1976.
I. Fary. On straight lines representation of planar graphs. Acta Sci. Math. Szeged., 11:229–233, 1948.
Qing-Wen Feng, Robert F. Cohen, and Peter Eades. How to draw a planar clustered graph. In COCOON'95, volume 959 of Lecture Notes in Computer Science, pages 21–31. Springer-Verlag, 1995.
Qing-Wen Feng, Robert F. Cohen, and Peter Eades. Planarity for clustered graphs. In ESA'95, volume 979 of Lecture Notes in Computer Science, pages 213–226. Springer-Verlag, 1995.
E.R. Gansner, S.C. North, and K.P. Vo. Dag — a program that draws directed graphs. Software — Practice and Experience, 18(11):1047–1062, 1988.
D. Harel. On visual formalisms. Communications of the ACM, 31(5):514–530, 1988.
Wei Lai. Building Interactive Digram Applications. PhD thesis, Department of Computer Science, University of Newcastle, Callaghan, New South Wales, Australia, 2308, June 1993.
Thomas Lengauer. Hierarchical planarity testing algorithms. Journal of ACM, 36:474–509, 1989.
Xuemin Lin. Analysis of Algorithms for Drawing Graphs. PhD thesis, Department of Computer Science, University of Queensland, Australia, 1992.
Franco P. Preparata and Michael I. Shamos. Computational geometry: an introduction. Springer-Verlag, New York, 1985.
R. Read. Methods for computer display and manipulation of graphs and the corresponding algorithms. Technical Report 86-12, Faculty of Mathematics, Univ. of Waterloo, July 1986.
S.K. Stein. Convex maps. Proceedings American Mathematical Society, 2:464–466, 1951.
K. Sugiyama and K. Misue. Visualization of structural information: Automatic drawing of compound digraphs. IEEE Transactions on Systems, Man and Cybernetics, 21(4):876–892, 1991.
K. Sugiyama, S. Tagawa, and M. Toda. Methods for visual understanding of hierarchical systems. IEEE Transactions on Systems, Man and Cybernetics, SMC-11(2):109–125, 1981.
W.T. Tutte. How to draw a graph. Proceedings London Mathematical Society, 3(13):743–768, 1963.
K. Wagner. Bemerkungen zum vierfarbenproblem. Jber. Deutsch. Math.-Verein, 46:26–32, 1936.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Eades, P., Feng, QW., Lin, X. (1997). Straight-line drawing algorithms for hierarchical graphs and clustered graphs. In: North, S. (eds) Graph Drawing. GD 1996. Lecture Notes in Computer Science, vol 1190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62495-3_42
Download citation
DOI: https://doi.org/10.1007/3-540-62495-3_42
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62495-0
Online ISBN: 978-3-540-68048-2
eBook Packages: Springer Book Archive