Abstract
The problems of nicely drawing planar graphs have received increasing attention due to their broad applications [5]. A technique, regular edge labeling, was successfully used in solving several planar graph drawing problems, including visibility representation, straight-line embedding, and rectangular dual problems. A regular edge labeling of a plane graph G labels the edges of G so that the edge labels around any vertex show certain regular pattern. The drawing of G is obtained by using the combinatorial structures resulting from the edge labeling. In this paper, we survey these drawing algorithms and discuss some open problems.
Research supported in part by NSF grant CCR-9205982.
Research supported in part by NSF grant CCR-9101385.
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References
J. Bhasker and S. Sahni, A linear algorithm to check for the existence of a rectangular dual of a planar triangulated graph, Networks 17, 1987, pp. 307–317.
J. Bhasker and S. Sahni, A linear algorithm to find a rectangular dual of a planar triangulated graph, Algorithmica 3, 1988, pp. 247–278.
N. Chiba, T. Yamanouchi, and T. Nishizeki, Linear algorithms for convex drawings of planar graphs, in Progress in Graph Theory, 1982, pp. 153–173.
M. Chrobak and T. H. Payne, A linear time algorithm for drawing planar graphs on a grid, TR. UCR-CS-90-2, Dept. of Math. and CS., Univ. of Calif. at Riverside.
P. Eades and R. Tamassia, Algorithms for automatic graph drawing: an annotated bibliography, TR., Dept. of Comp. Sci., Brown Univ., 1993.
H. de Fraysseix, J. Pach and R. Pollack, How to draw a planar graph on a grid, Combinatorica 10 (1990), pp. 41–51.
H. de Fraysseix, J. Pach and R. Pollack, Small sets supporting Fáry embeddings of planar graphs, Proc. of the 20th ACM STOC, 1988, pp. 426–433.
I. Fáry, On straight line representation of planar graphs, Acta Sci Math Szeged, 11 (1948), pp. 229–233.
M. Fürer, X. He, M. Y. Kao, and B. Raghavachari, O(n log log n)-work parallel algorithms for straight-line grid embeddings of planar graphs, Proc. of 4th ACM SPAA, 1992, pp. 410–419. Improved version to appear in SIAM J. Discrete Math.
X. He, On finding the rectangular duals of planar triangulated graphs, SIAM J. Comput. 22 (6), 1993, pp. 1218–1226.
X. He, An efficient parallel algorithm for finding rectangular duals of planar triangular graphs, Proc. 3rd International Conference for Young Computer Scientists, Beijing, 1993, pp. 6.33–6.37. Complete version to appear in Algorithmica.
W. R. Heller, G. Sorkin and K. Mailing, The planar package planner for system designers, Proc. 19th IEEE Design Automation Conf., 1982, pp. 253–260.
G. Kant, Drawing planar graphs using the lmc-ordering, in Proc. 33th Ann. IEEE Symp. on Found. of Comp. Science, Pittsburgh, 1992, pp. 101–110.
G. Kant, A more compact visibility representation, in: J. van Leeuwen (Ed.), Proc. 19th Intern. Workshop on Graph-Theoretic Concepts in Comp. Science (WG'93).
G. Kant and X. He, Two algorithms for finding rectangular duals of planar graphs, in: J. van Leeuwen (Ed.), Proc. 19th Intern. Workshop on Graph-Theoretic Concepts in Comp. Science (WG'93), LNCS, Springer-Verlag, 1994, to appear.
K. Koźmiński and E. Kinnen, Rectangular dual of planar graphs, Networks 15, 1985, pp. 145–157.
Y.-T. Lai and S. M. Leinwand, A theory of rectangular dual graphs, Algorithmica 5, 1990, pp. 467–483.
F. P. Preparata and R. Tamassia, Fully dynamic techniques for point location and transitive closure in planar structures, Proc. 29th FOCS, 1988, pp. 558–567.
R. C. Read, A new method for drawing a planar graph given the cyclic order of the edges at each vertex, Congressus Numerantium 56 (1987), pp. 31–44.
P. Rosenstiehl and R. E. Tarjan, Rectilinear planar layouts and bipolar orientations of planar graphs, Discr. and Comp. Geometry 1, 1986, pp. 343–353.
W. Schnyder, Embedding planar graphs on the grid, Abstracts of the Amer. Math. Soc., 9 (1988), p. 268.
W. Schnyder, Planar graphs and poset dimension, Orders 5 (1989), pp. 323–343.
W. Schnyder, Embedding planar graphs on the grid, in Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, 1990, pp. 138–148.
S. K. Stein, Convex maps, in Proc Amer Math Soc, vol. 2, 1951, pp. 464–466.
R. Tamassia and J. S. Vitter, Parallel transitive closure and point location in planar structures, SIAM J. Comput. 20 (2), 1991, pp. 708–725.
R. Tamassia, Drawing Algorithms for Planar s-t Graphs, Australasian Journal of Combinatorics, Vol. 2, 1990, pp. 217–236.
R. Tamassia and I. Tollis, Tessellation Representations of Planar Graphs, in Proc. 27th Allerton Conference, 1989, pp. 48–57.
R. Tamassia and I. G. Tollis, A unified approach to visibility representations of planar graphs, Discr. and Comp. Geometry 1, 1986, pp. 321–341.
R. Tamassia and I. G. Tollis, Planar grid embedding in linear time, IEEE Trans. Circuits and Systems 36, 1989, pp. 1230–1234.
W. Tutte, How to draw a graph, Proc. London Math. Soc. 13, 1963, pp. 743–768.
K. Wagner, Bemerkungen zum Vierfarbenproblem, Jahresbericht Deutsch Math-Verein, 46 (1936), pp. 26–32.
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He, X., Kao, MY. (1995). Regular edge labelings and drawings of planar graphs. In: Tamassia, R., Tollis, I.G. (eds) Graph Drawing. GD 1994. Lecture Notes in Computer Science, vol 894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58950-3_360
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