Abstract
The visualization of graphs is a key component for many applications in science and engineering. When drawing a graph, we would like to take into account several aesthetic criteria. For example, planarity and the display of symmetries are often highly desirable in visualization applications. Also, to avoid wasting space on the screen, it is important to keep the area of the drawing small, subject to resolution rules. Further, it is desirable to avoid as much as possible long edges with bends.
Many graph drawing problems can be formalized as optimization problems. Solving better or worse such problems implies constructing drawings with better or worse aesthetic features. On the other hand, finding satisfactory solutions requires very often the usage of substantial computational resources. For this reason the research in graph drawing continuosly explores the aesthetics-complexity trade-off. Examples can be found in the construction of drawings with a few bends along the edges, where the commonly used techniques cover a large time-compexity interval that includes polynomial-time and exponential-time algorithms.
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References
P. Bertolazzi, G. Di Battista, and W. Didimo. Computing orthogonal drawings with the minimum number of bends. In F. Dehne, A. Rau-Chaplin, J.-R. Sack, and R. Tamassia, editors, Proc. 5th Workshop Algorithms Data Struct., volume 1272 of Lecture Notes Comput. Sci., pages 331–344. Springer-Verlag, 1997.
T. Biedl and G. Kant. A better heuristic for orthogonal graph drawings. In Proc. 2nd Annu. European Sympos. Algorithms, volume 855 of Lecture Notes Comput. Sci., pages 24–35. Springer-Verlag, 1994.
G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing. Prentice Hall, Upper Saddle River, NJ, 1999.
G. Di Battista and R. Tamassia. On-line planarity testing. SIAM J. Comput, 25:956–997, 1996.
A. Garg and R. Tamassia. On the computational complexity of upward and rectilinear planarity testing. In R. Tamassia and I. G. Tollis, editors, Graph Drawing (Proc. GD ′94), volume 894 of Lecture Notes Comput Sci., pages 286–297. Springer-Verlag, 1995.
A. Garg and R. Tamassia. A new minimum cost flow algorithm with applications to graph drawing. In S. C. North, editor, Graph Drawing (Proc. GD ′96), volume 1190 of Lecture Notes Comput Sci., pages 201–216. Springer-Verlag, 1997.
M. Jünger and P. Mutzel. The polyhedral approach to the maximum planar subgraph problem: New chances for related problems. In R. Tamassia and I. G. Tollis, editors, Graph Drawing (Proc. GD ′94), volume 894 of Lecture Notes Comput Sci., pages 119–130. Springer-Verlag, 1995.
R. Tamassia. On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput., 16(3):421–444, 1987.
R. Tamassia and I. G. Tollis. Efficient embedding of planar graphs in linear time. In Proc. IEEE Internat. Sympos. on Circuits and Systems, pages 495–498, 1987.
R. Tamassia and I. G. Tollis. Planar grid embedding in linear time. IEEE Trans. Circuits Syst, CAS-36(9):1230–1234, 1989.
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Di Battista, G. (2000). Graph Drawing: the Aesthetics-Complexity Trade-Off. In: Inderfurth, K., Schwödiauer, G., Domschke, W., Juhnke, F., Kleinschmidt, P., Wäscher, G. (eds) Operations Research Proceedings 1999. Operations Research Proceedings 1999, vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58300-1_17
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