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Advances in graph drawing

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Algorithms and Complexity (CIAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 778))

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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

  1. T. Andreae. Some results on visibility graphs. Discrete Applied Mathematics, 40:5–17, 1992.

    Google Scholar 

  2. 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.

    Google Scholar 

  3. 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.

    Google Scholar 

  4. P. Bertolazzi, G. Di Battista, G. Liotta, and C. Mannino. Upward drawings of triconnected digraphs. Algorithmica, to appear.

    Google Scholar 

  5. 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.

    Google Scholar 

  6. 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.

    Google Scholar 

  7. R.P. Brent and H.T. Kung. On the area of binary tree layouts. Information Processing Letters, 11:521–534, 1980.

    Google Scholar 

  8. 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.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. 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.

    Google Scholar 

  11. I. F. Cruz. DOODLE: A visual language for object-oriented databases. In Proc. ACM SIGMOD, pages 71–80, 1992.

    Google Scholar 

  12. 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.

    Google Scholar 

  13. 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.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. H. de Fraysseix, J. Pach, and R. Pollack. How to draw a planar graph on a grid. Combinatorica, 10:41–51, 1990.

    Google Scholar 

  16. H. de Fraysseix and P. Rosenstiehl. A depth-first-search characterization of planarity. Annals of Discrete Mathematics, 13:75–80, 1982.

    Google Scholar 

  17. 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.

    Google Scholar 

  18. 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.

    Google Scholar 

  19. 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.

    Google Scholar 

  20. 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.

    Google Scholar 

  21. G. Di Battista, W. P. Liu, and I. Rival. Bipartite graphs upward drawings and planarity. Inform. Process, Lett., 36:317–322, 1990.

    Google Scholar 

  22. G. Di Battista and R. Tamassia. Algorithms for plane representations of acyclic digraphs. Theoret. Comput. Sci., 61:175–198, 1988.

    Google Scholar 

  23. 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.

    Google Scholar 

  24. 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.

    Google Scholar 

  25. 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.

    Google Scholar 

  26. 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.

    Google Scholar 

  27. 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.

    Google Scholar 

  28. A. Garg and R. Tamassia. Angular resolution of planar drawings. Technical report, Brown Univ., Dept. of Computer Science, 1993.

    Google Scholar 

  29. A. Garg and R. Tamassia. On the complexity of upward planarity testing. Technical report, Brown Univ., Dept. of Computer Science, 1993.

    Google Scholar 

  30. J. Hopcroft and R. E. Tarjan. Efficient planarity testing. J. ACM, 21(4):549–568, 1974.

    Google Scholar 

  31. 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.

    Google Scholar 

  32. T. Kamada. Visualizing Abstract Objects and Relations. World Scientific Series in Computer Science, 1989.

    Google Scholar 

  33. G. Kant. Drawing planar graphs using the lmc-ordering. In Proc. 33th Annu. IEEE Sympos. Found. Comput. Sci., pages 101–110, 1992.

    Google Scholar 

  34. G. Kant. A more compact visibility representation. In Proc. 19th Internat. Workshop Graph-Theoret. Concepts Comput. Sci. (WG'93), 1993.

    Google Scholar 

  35. 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.

    Google Scholar 

  36. D. Kelly. Fundamentals of planar ordered sets. Discrete Math., 63:197–216, 1987.

    Google Scholar 

  37. D. Kelly and I. Rival. Planar lattices. Canad. J. Math., 27(3):636–665, 1975.

    Google Scholar 

  38. 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.

    Google Scholar 

  39. C. E. Leiserson. Area-efficient graph layouts (for VLSI). In Proc. 21st Annu. IEEE Sympos. Found. Comput. Sci., pages 270–281, 1980.

    Google Scholar 

  40. 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.

    Google Scholar 

  41. S. Malitz and A. Papakostas. On the angular resolution of planar graphs. In Proc. 24th Annu. ACM Sympos. Theory Comput., pages 527–538, 1992.

    Google Scholar 

  42. J. Marks. A formal specification for network diagrams that facilitates automated design. Journal of Visual Languages and Computing, 26:395–414, 1991.

    Google Scholar 

  43. J. O'Rourke. Art Gallery Theorems and Algorithms. Oxford University Press, New York, NY, 1987.

    Google Scholar 

  44. C. Platt. Planar lattices and planar graphs. J. Combin. Theory Ser. B, 21:30–39, 1976.

    Google Scholar 

  45. F. P. Preparata and M. I. Shamos. Computational Geometry: an Introduction. Springer-Verlag, New York, NY, 1985.

    Google Scholar 

  46. I. Rival. Graphical data structures for ordered sets. In I. Rival, editor, Algorithms and Order, pages 3–31. Kluwer Academic Publishers, 1989.

    Google Scholar 

  47. P. Rosenstiehl and R. E. Tarjan. Rectilinear planar layouts and bipolar orientations of planar graphs. Discrete Comput. Geom., 1(4):343–353, 1986.

    Google Scholar 

  48. W. Schnyder. Embedding planar graphs on the grid. In Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pages 138–148, 1990.

    Google Scholar 

  49. T. C. Shermer. Recent results in art galleries. Proc. IEEE, 80(9):1384–1399, September 1992.

    Google Scholar 

  50. 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.

    Google Scholar 

  51. R. Tamassia and I. G. Tollis. A unified approach to visibility representations of planar graphs. Discrete Comput. Geom., 1(4):321–341, 1986.

    Google Scholar 

  52. C. Thomassen. Planar acyclic oriented graphs. Order, 5(4):349–361, 1989.

    Google Scholar 

  53. L. Valiant. Universality considerations in VLSI circuits. IEEE Trans. Comput., C-30(2):135–140, 1981.

    Google Scholar 

  54. S. K. Wismath. Characterizing bar line-of-sight graphs. In Proc. 1st Annu. ACM Sympos. Comput. Geom., pages 147–152, 1985.

    Google Scholar 

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M. Bonuccelli P. Crescenzi R. Petreschi

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© 1994 Springer-Verlag Berlin Heidelberg

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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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  • DOI: https://doi.org/10.1007/3-540-57811-0_2

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  • Online ISBN: 978-3-540-48337-3

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