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European Symposium on Algorithms

ESA 1996: Algorithms — ESA '96 pp 12–26Cite as

Drawing with colors

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1136))

Abstract

In this paper, we investigate the volume, aspect ratio, angular resolution, edge-separation, and bit-requirement of crossing-free straight-line 3D drawings. We assume the vertex resolution rule, which requires minimum unit distance between any two vertices. Our main result shows that an N-vertex graph colorable with O(1) colors admits a crossing-free straight-line 3D drawing with O(N√N) volume, O(1) aspect ratio,gW(l/N O(1)) angular resolution, Ω (1/N O(1)) edge-separation, and O(log N) bit-requirement, which can be constructed in O(N) time.

Research supported in part the National Science Foundation under grant CCR-9423847, by the U.S. Army Research Office under grant DAAH04-96-1-0013, and by a gift from Tom Sawyer Software. Research performed in part while Paola Vocca was visiting Brown University, and while Roberto Tamassia and Paola Vocca were visiting the Bellairs Research Institute of McGill University.

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References

  1. H. Alt, M. Godau, and S. Whitesides. Universal 3-dimensional visibility representations for graphs. In F. J. Brandenburg, editor, Graph Drawing (Proc. GD '95), volume 1027 of Lecture Notes in Computer Science, pages 8–19. Springer-Verlag, 1996.

    Google Scholar 

  2. I. Bruß and A. Frick. Fast interactive 3-d graph visualization. In F. Brandenburg, editor, Graph Drawing (Proc. GD '95), volume 1027 of LNCS, pages 99–110, 1996.

    Google Scholar 

  3. T. Calamoneri and A. Sterbini. Drawing 2-, 3-and 4-colorable graphs in o(n 2) volume. Technical report, Dept. of Comp. Sc., Univ. Rome “La Sapienza”, 1996.

    Google Scholar 

  4. M. Chrobak, M. T. Goodrich, and R. Tamassia. Convex drawings of graphs in two and three dimensions. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 319–328, 1996.

    Google Scholar 

  5. R. F. Cohen, P. Eades, T. Lin, and F. Ruskey. Three-dimensional graph drawing. In R. Tamassia and I. G. Tollis, editors, Graph Drawing (Proc. GD '94), volume 894 of Lecture Notes in Computer Science, pages 1–11. Springer-Verlag, 1995.

    Google Scholar 

  6. I. Cruz and J. Twarog. 3d graph drawing with simulated annealing. In F. Brendenburg, editor, Graph Drawing (Proc. GD '95), volume 1027 of Lecture Notes in Computer Science, pages 162–165. Springer-Verlag, 1996.

    Google Scholar 

  7. G. Das and M. T. Goodrich. On the complexity of approximating and illuminating three-dimensional convex polyhedra. In Proc. 4th Workshop Algorithms Data Struct., volume 955 of Lecture Notes in Computer Science, pages 74–85. Springer-Verlag, 1995.

    Google Scholar 

  8. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Algorithms for drawing graphs: an annotated bibliography. Comput. Geom. Theory Appl, 4:235–282, 1994.

    Google Scholar 

  9. P. Eades and P. Garvan. Drawing stressed planar graphs in three dimensions. In F. J. Brandenburg, editor, Graph Drawing (Proc. GD '95), volume 1027 of Lecture Notes in Computer Science. Springer-Verlag, 1996.

    Google Scholar 

  10. P. Eades, C. Stirk, and S. Whitesides. The techniques of Komolgorov and Bardzin for three dimensional orthogonal graph drawings. Manuscript, Dept. of Computer Sci., Univ. of Newcastle, 1995.

    Google Scholar 

  11. 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. SIAM J. Comput, 22:1035–1052, 1993.

    Google Scholar 

  12. A. Garg and R. Tamassia. Area-optimal upward tree drawings. Int. Journal of Computational Geometry: Theory and Applns. to appear.

    Google Scholar 

  13. S. M. Hashemi and I. Rival. Upward drawings to fit surfaces. In Order, Algorithms, and Applications (Proc. ORDAL '94), volume 831 of Lecture Notes in Computer Science, pages 53–58. Springer-Verlag, 1994.

    Google Scholar 

  14. D. Jablonowsky and V. A. Guarna. GMB: A tool for manipulating and animating graph data structures. Softw. — Pract. Exp., 19(3):283–301, 1989.

    Google Scholar 

  15. T. Jéron and C. Jard. 3D layout of reachability graphs of communicating processes. In R. Tamassia and I. G. Tollis, editors, Graph Drawing (Proc. GD '94), volume 894 of Lecture Notes in Computer Science, pages 25–32. Springer-Verlag, 1995.

    Google Scholar 

  16. F. T. Leighton and A. Rosenberg. 3d circuit layouts. SIAM J. Comput., 15:793–813, 1986.

    Google Scholar 

  17. G. Liotta and G. Di Battista. Computing proximity drawings of trees in the 3-dimemsional space. In Proc. 4th Workshop Algorithms Data Struct., volume 955 of Lecture Notes in Computer Science, pages 239–250. Springer-Verlag, 1995.

    Google Scholar 

  18. B. Monien, F. Ramme, and H. Salmen. A parallel simulated annealing algorithm for generating 3d layouts of undirected graphs. In F. Brandenburg, editor, Graph Drawing (Proc. GD '95), volume 1027 of LNCS, pages 396–408, 1996.

    Google Scholar 

  19. S. P. Reiss. An engine for the 3D visualization of program information. J. Visual Languages and Computing, 6(3), 1995. (special issue on Graph Visualization, edited by I. F. Cruz and P. Eades).

    Google Scholar 

  20. G. G. Robertson, J. D. Mackinlay, and S. K. Card. Cone trees: Animated 3d visualizations of hierarchical information. In Proc. CHI, pages 189–193, 1991.

    Google Scholar 

  21. A. L. Rosenberg. Three-dimensional VLSI: a case study. J. ACM, 30(3):397–416, 1983.

    Google Scholar 

  22. E. Steinitz and H. Rademacher. Vorlesungen über die Theorie der Polyeder. Julius Springer, Berlin, Germany, 1934.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Center for Geometric Computing Department of Computer Science, Brown University, 02912-1910, Providence, RI, USA

    Ashim Garg & Roberto Tamassia

  2. Dipartimento di Matematica, University of Rome “Tor Vergata”, via della Ricerca Scientifica, 00133, Rome, Italy

    Paola Vocca

Authors
  1. Ashim Garg
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  2. Roberto Tamassia
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  3. Paola Vocca
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Editor information

Josep Diaz Maria Serna

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© 1996 Springer-Verlag Berlin Heidelberg

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Garg, A., Tamassia, R., Vocca, P. (1996). Drawing with colors. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_43

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  • DOI: https://doi.org/10.1007/3-540-61680-2_43

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61680-1

  • Online ISBN: 978-3-540-70667-0

  • eBook Packages: Springer Book Archive

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