Abstract
Graph drawing addresses the problem of constructing geometric representations of abstract graphs and networks. It is an emerging area of research that combines flavors of topological graph theory and computational geometry. The automatic generation of drawings of graphs has important applications in key computer technologies such as software engineering, database design, visual interfaces, and computer-aided-design. This paper surveys recent results of the authors on graph drawing and overviews various research trends in the area.
Research supported in part by the National Science Foundation under grant CCR-9007851, by the U.S. Army Research Office under grant DAAL03-91-G-0035, and by the Office of Naval Research and the Advanced Research Projects Agency under contract N00014-91-J-4052, ARPA order 8225.
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References
T. Andreae. Some results on visibility graphs. Discrete Applied Mathematics, 40:5–17, 1992.
M. Beccaria, P. Bertolazzi, G. Di Battista, and G. Liotta. A tailorable and extensible automatic layout facility. In Proc. IEEE Workshop on Visual Languages (VL'91), pages 68–73, 1991.
P. Bertolazzi and G. Di Battista. On upward drawing testing of triconnected digraphs. In Proc. 7th Annu. ACM Sympos. Comput. Geom, pages 272–280, 1991.
P. Bertolazzi, G. Di Battista, G. Liotta, and C. Mannino. Upward drawings of triconnected digraphs. Algorithmica, to appear.
P. Bertolazzi, G. Di Battista, C. Mannino, and R. Tamassia. Optimal upward planarity testing of single-source digraphs. In 1st Annual European Symposium on Algorithms (ESA '93), Lecture Notes in Computer Science. Springer-Verlag, 1993.
K. Booth and G. Lueker. Testing for the consecutive ones property interval graphs and graph planarity using PQ-tree algorithms. J. Comput. Syst. Sci., 13:335–379, 1976.
R.P. Brent and H.T. Kung. On the area of binary tree layouts. Information Processing Letters, 11:521–534, 1980.
M. Chrobak and T. H. Payne. A linear time algorithm for drawing a planar graph on a grid. Technical Report UCR-CS-90-2, Dept. of Math. and Comput. Sci., Univ. California Riverside, 1990.
R. F. Cohen, G. Di Battista, R. Tamassia, I. G. Tollis, and P. Bertolazzi. A framework for dynamic graph drawing. In Proc. 8th Annu. ACM Sympos. Comput. Geom., pages 261–270, 1992.
P. Crescenzi, G. Di Battista, and A. Piperno. A note on optimal area algorithms for upward drawings of binary trees. Computational Geometry: Theory and Applications, 2:187–200, 1992.
I. F. Cruz. DOODLE: A visual language for object-oriented databases. In Proc. ACM SIGMOD, pages 71–80, 1992.
I. F. Cruz. Using a visual constraint language for data display specification. In P. C. Kanellakis, J.-L. Lassez, and V. Saraswat, editors, First Workshop on Principles and Practice of Constraint Programming, Newport, RI, April 1993.
I. F. Cruz, R. Tamassia, and P. Van Hentenryk. A visual approach to graph drawing. In Graph Drawing '93 (Proc. ALCOM Workshop on Graph Drawing), Paris, France, September 1993.
H. de Fraysseix, J. Pach, and R. Pollack. Small sets supporting Fary embeddings of planar graphs. In Proc. 20th Annu. ACM Sympos. Theory Comput., pages 426–433, 1988.
H. de Fraysseix, J. Pach, and R. Pollack. How to draw a planar graph on a grid. Combinatorica, 10:41–51, 1990.
H. de Fraysseix and P. Rosenstiehl. A depth-first-search characterization of planarity. Annals of Discrete Mathematics, 13:75–80, 1982.
G. Di Battista, P. Eades, H. de Fraysseix, P. Rosenstiehl, and R. Tamassia. Graph Drawing '93 (Proc. ALCOM Int. Workshop on Graph Drawing). 1993. Available via anonymous ftp from wilma.cs.brown.edu, /pub/papers/compgeo/gd93-v2.tex.Z.
G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Algorithms for drawing graphs: an annotated bibliography. Preprint, Dept. Comput. Sci., Brown Univ., Providence, RI, November 1993. To appear in Comput. Geom. Theory Appl. Preliminary version available via anonymous ftp from wilma.cs.brown.edu, gdbiblio.tex.Z and gdbiblio.ps.Z in /pub/papers/compgeo.
G. Di Battista, A. Giammarco, G. Santucci, and R. Tamassia. The architecture of diagram server. In Proc. IEEE Workshop on Visual Languages (VL'90), pages 60–65, 1990.
G. Di Battista, G. Liotta, M. Strani, and F. Vargiu. Diagram server. In Advanced Visual Interfaces (Proceedings of AVI '92), volume 36 of World Scientific Series in Computer Science, pages 415–417, 1992.
G. Di Battista, W. P. Liu, and I. Rival. Bipartite graphs upward drawings and planarity. Inform. Process, Lett., 36:317–322, 1990.
G. Di Battista and R. Tamassia. Algorithms for plane representations of acyclic digraphs. Theoret. Comput. Sci., 61:175–198, 1988.
G. Di Battista, R. Tamassia, and I. G. Tollis. Area requirement and symmetry display of planar upward drawings. Discrete Comput. Geom., 7:381–401, 1992.
G. Di Battista and L. Vismara. Angles of planar triangular graphs. In Proc. 25th Annu. ACM Sympos. Theory Comput. (STOC 93), pages 431–437, 1993.
P. Eades and T. Lin. Algorithmic and declarative approaches to aesthetic layout. In Graph Drawing '93 (Proc. ALCOM Workshop on Graph Drawing), Paris, France, September 1993.
M. Formann, T. Hagerup, J. Haralambides, M. Kaufmann, F. T. Leighton, A. Simvonis, E. Welzl, and G. Woeginger. Drawing graphs in the plane with high resolution. In Proc. 31th Annu. IEEE Sympos. Found. Comput. Sci., pages 86–95, 1990.
A. Garg, M. T. Goodrich, and R. Tamassia. Area-efficient upward tree drawings. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 359–368, 1993.
A. Garg and R. Tamassia. Angular resolution of planar drawings. Technical report, Brown Univ., Dept. of Computer Science, 1993.
A. Garg and R. Tamassia. On the complexity of upward planarity testing. Technical report, Brown Univ., Dept. of Computer Science, 1993.
J. Hopcroft and R. E. Tarjan. Efficient planarity testing. J. ACM, 21(4):549–568, 1974.
M. D. Hutton and A. Lubiw. Upward planar drawing of single source acyclic digraphs. In Proc. 2nd ACM-SIAM Sympos. Discrete Algorithms, pages 203–211, 1991.
T. Kamada. Visualizing Abstract Objects and Relations. World Scientific Series in Computer Science, 1989.
G. Kant. Drawing planar graphs using the lmc-ordering. In Proc. 33th Annu. IEEE Sympos. Found. Comput. Sci., pages 101–110, 1992.
G. Kant. A more compact visibility representation. In Proc. 19th Internat. Workshop Graph-Theoret. Concepts Comput. Sci. (WG'93), 1993.
G. Kant, G. Liotta, R. Tamassia, and I. Tollis. Area requirements of visibility representations of trees. In Proc. 5th Canad. Conf. Comput. Geom., pages 192–197, Waterloo, Canada, 1993.
D. Kelly. Fundamentals of planar ordered sets. Discrete Math., 63:197–216, 1987.
D. Kelly and I. Rival. Planar lattices. Canad. J. Math., 27(3):636–665, 1975.
D. G. Kirkpatrick and S. K. Wismath. Weighted visibility graphs of bars and related flow problems. In Proc. 1st Workshop Algorithms Data Struct., volume 382 of Lecture Notes in Computer Science, pages 325–334. Springer-Verlag, 1989.
C. E. Leiserson. Area-efficient graph layouts (for VLSI). In Proc. 21st Annu. IEEE Sympos. Found. Comput. Sci., pages 270–281, 1980.
A. Lempel, S. Even, and I. Cederbaum. An algorithm for planarity testing of graphs. In Theory of Graphs: Internat. Symposium (Rome 1966), pages 215–232, New York, 1967. Gordon and Breach.
S. Malitz and A. Papakostas. On the angular resolution of planar graphs. In Proc. 24th Annu. ACM Sympos. Theory Comput., pages 527–538, 1992.
J. Marks. A formal specification for network diagrams that facilitates automated design. Journal of Visual Languages and Computing, 26:395–414, 1991.
J. O'Rourke. Art Gallery Theorems and Algorithms. Oxford University Press, New York, NY, 1987.
C. Platt. Planar lattices and planar graphs. J. Combin. Theory Ser. B, 21:30–39, 1976.
F. P. Preparata and M. I. Shamos. Computational Geometry: an Introduction. Springer-Verlag, New York, NY, 1985.
I. Rival. Graphical data structures for ordered sets. In I. Rival, editor, Algorithms and Order, pages 3–31. Kluwer Academic Publishers, 1989.
P. Rosenstiehl and R. E. Tarjan. Rectilinear planar layouts and bipolar orientations of planar graphs. Discrete Comput. Geom., 1(4):343–353, 1986.
W. Schnyder. Embedding planar graphs on the grid. In Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pages 138–148, 1990.
T. C. Shermer. Recent results in art galleries. Proc. IEEE, 80(9):1384–1399, September 1992.
R. Tamassia, G. Di Battista, and C. Batini. Automatic graph drawing and readability of diagrams. IEEE Trans. Syst. Man Cybern., SMC-18(1):61–79, 1988.
R. Tamassia and I. G. Tollis. A unified approach to visibility representations of planar graphs. Discrete Comput. Geom., 1(4):321–341, 1986.
C. Thomassen. Planar acyclic oriented graphs. Order, 5(4):349–361, 1989.
L. Valiant. Universality considerations in VLSI circuits. IEEE Trans. Comput., C-30(2):135–140, 1981.
S. K. Wismath. Characterizing bar line-of-sight graphs. In Proc. 1st Annu. ACM Sympos. Comput. Geom., pages 147–152, 1985.
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Garg, A., Tamassia, R. (1994). Advances in graph drawing. In: Bonuccelli, M., Crescenzi, P., Petreschi, R. (eds) Algorithms and Complexity. CIAC 1994. Lecture Notes in Computer Science, vol 778. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57811-0_2
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