Zusammenfassung
Zeichnungen sind nicht nur ein ansprechendes, sondern auch ein sehr effektives Mittel, um die durch einen Graphen repräsentierte Information zu vermitteln. Der geeignete Entwurf solcher Zeichnungen ist jedoch schon bei kleinen Graphen eine schwierige und zeitraubende Arbeit, die nach Automatisierung geradezu ruft. Wir leiten daher eine Formalisierung des Problems her und stellen anhand von Anwendungen aus der Soziologie und dem Verkehrswesen Möglichkeiten des automatischen Zeichnens dar.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literatur
E. H. L. Aarts und J. H. M. Korst. Simulated Annealing and Boltzmann Machines. Wiley, 1989.
S. D. Berkowitz. An Introduction to Structural Analysis: The Network Approach to Scocial Research. Butterworths, 1982.
J. Besag. On the statistical analysis of dirty pictures. Journal of the Royal Statistical Society, Series B, 48(3):259–302, 1986.
F. J. Brandenburg (ed.). Proceedings of the 3rd International Symposium on Graph Drawing (GD’ 95), Lecture Notes in Computer Science, Nr. 1027. Springer, 1996.
F. J. Brandenburg, M. Himsolt und C. Rohrer. An experimental comparison of force-directed and randomized graph drawing algorithms. In [4], Seiten 76-87.
U. Brandes, P. Kenis, J. Raab, V. Schneider und D. Wagner. Explorations into the visualization of policy networks. Erscheint in Journal of Theoretical Politics, 11(1), 1999.
U. Brandes und D. Wagner. A Bayesian paradigm for dynamic graph layout. In [16], Seiten 236-247.
U. Brandes und D. Wagner. Random field models for graph layout. Konstanzer Schriften in Mathematik und Informatik, Nr. 33. Universität Konstanz, April 1997.
U. Brandes und D. Wagner. Dynamic grid embedding with few bends and changes. In K.-Y. Chwa und O. H. Ibarra (eds.), Proceedings of the 9th Annual International Symposium on Algorithms and Computation (ISAAC’ 98), Lecture Notes in Computer Science, Nr. 1533, Seiten 89-98. Springer, 1998.
U. Brandes und D. Wagner. Using graph layout to visualize train interconnection data. Erscheint in [47].
G. R. Brightwell und E. R. Scheinerman. Representations of planar graphs. SIAM Journal on Discrete Mathematics, 6(2):214–229, Mai 1993.
I. Bruß und A. Frick. Fast interactive 3-D graph visualization. In [4], Seiten 99-110.
R. S. Burt. Toward a Structural Theory of Action: Network Models of Social Structure, Perception, and Action. Academic Press, 1982.
I. F. Cruz und J. P. Twarog. 3D graph drawing with simulated annealing. In [4], Seiten 162-165.
R. Davidson und D. Harel. Drawing graphs nicely using simulated annealing. ACM Transactions on Graphics, 15(4):301–331, 1996.
G. Di Battista (ed.). Proceedings of the 5th International Symposium on Graph Drawing (GD’ 97), Lecture Notes in Computer Science, Nr. 1353. Springer, 1997.
G. Di Battista, P. Eades, H. de Fraysseix, P. Rosenstiehl und R. Tamassia, (eds.). Proceedings of the ALCOM International Workshop on Graph Drawing (GD’ 93), 1993. ftp.cs.brown.edu/pub/gd94/gd-92-93/gd93-v2.ps.Z.
G. Di Battista, P. Eades, R. Tamassia und I. G. Tollis. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, 1999.
P. Eades. A heuristic for graph drawing. Congressus Numerantium, 42:149–160, 1984.
P. Eades, J. Marks und S. C. North. Graph-drawing contest report. In [16], Seiten 438-445.
C. J. Fisk, D. L. Caskey und L. E. West. ACCEL: Automated circuit card etching layout. Proceedings of the IEEE, 55(11):1971–1982, November 1967.
L. C. Freeman. Centrality in social networks: Conceptual clarification. Social Networks, 1:215–239,1979.
A. Frick, A. Ludwig und H. Mehldau. A fast adaptive layout algorithm for undirected graphs. In [40], Seiten 388-403.
T. M. J. Fruchterman und E. M. Reingold. Graph-drawing by force-directed placement. Software—Practice and Experience, 21(11):1129–1164, 1991.
A. Garg. On drawing angle graphs. In [40], Seiten 84-95.
M. R. Garey und D. S. Johnson. Crossing Number is NP-Complete. SIAM Journal on Algebraic Discrete Methods, 4(3):312–316, 1983.
D. S. Johnson. The NP-completeness column: An ongoing guide. Journal of Algorithms, 3:89–99, 1982.
T. Kamada und S. Kawai. An algorithm for drawing general undirected graphs. Information Processing Letters, 31:7–15, 1989.
T. Kamps, J. Kleinz und J. Read. Constraint-based spring-model algorithms for graph layout. In [4], Seiten 349-360.
S. Kirckpatrick, C. D. Gelatt und M. P. Vecchi. Optimization by simulated annealing. Science, 220(4598):671–680, Mai 1983.
Donald E. Knuth. Computer Drawn Flowcharts. Communications of the ACM, 6(9):555–563, 1963
J. A. McDonald und J. Pedersen. Geometric abstractions for constrained optimization of layouts. In A. Buja und P. A. Tukey (eds.), Computing and Graphics in Statistics, The IMA Volumes in Mathematics and its Applications, Nr. 36, pages 95–105. Springer, 1991.
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller und E. Teller. Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21(6): 1087–1092, Juni 1953.
S. C. North (ed.). Proceedings of the 4th International Symposium on Graph Drawing (GD’ 96), Lecture Notes in Computer Science, Nr. 1190. Springer, 1996.
W. D. Niven (ed.). The Scientific Papers of James Clark Maxwell, Dover Publications, New York, 1965.
J. F. Padgett und C. K. Ansell. Robust action and the rise of the Medici, 1400–1434. American Journal of Sociology 98:1259–1319, 1993.
N. R. Quinn und M. A. Breuer. A force directed component placement procedure for printed circuit boards. IEEE Transactions on Circuits and Systems, 26(6):377–388, 1979.
J. Scott. Social Network Analysis: A Handbook. Sage Publications, 1991.
K. Sugiyama und K. Misue. A simple and unified method for drawing graphs: Magnetic-spring algorithm. In [40], Seiten 364-375.
R. Tamassia und I. G. Tollis (eds.). Proceedings of the 2nd International Symposium on Graph Drawing (GD’ 94), Lecture Notes in Computer Science, Nr. 894. Springer, 1995.
E. R. Tufte. Envisioning Information. Graphics Press, 1990.
D. Tunkelang. A practical approach to drawing undirected graphs. Technical Report CMU-CS-94-161, School of Computer Science, Carnegie Mellon University, Juni 1994.
W. T. Tutte. How to draw a graph. Proceedings of the London Mathematical Society, Third Series, 13:743–768, 1963.
P. J. M. van Laarhoven und E. H. L. Aarts. Simulated Annealing: Theory and Applications. Reidel, 1988.
S. Wasserman und K. Faust. Social Network Analysis: Methods and Applications. Cambridge University Press, 1994.
R. Webber. Finding the Best Viewpoint for Three-Dimensional Graph Drawings. PhD thesis, University of Newcastle, 1998.
S. H. Whitesides (ed.). Proceedings of the 6th International Symposium on Graph Drawing (GD’ 98), Lecture Notes in Computer Science, Nr. 1547. Springer, 1998.
G. Winkler. Image Analysis, Random Fields and Dynamic Monte Carlo Methods, Applications of Mathematics, Nr. 27. Springer, 1995.
D. Wood. On higher-dimensional orthogonal graph drawing. Technical Report 96/286, Department of Computer Science, Monash University, November 1996.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
About this chapter
Cite this chapter
Brandes, U., Wagner, D. (1999). Über das Zeichnen von Graphen. In: Horster, P. (eds) Angewandte Mathematik, insbesondere Informatik. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-83092-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-322-83092-0_5
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-528-05720-6
Online ISBN: 978-3-322-83092-0
eBook Packages: Springer Book Archive