Planar upward tree drawings with optimal area

International Journal of Computational Geometry and Applications

Volumn 6, Issue 3, 1996, Pages 333-356

  Garg, Ashim ^a   Goodrich, Michael T ^b   Tamassia, Roberto ^a  

^a Brown Univerity   (United States)

^b Johns Hopkins University   (United States)

Author keywords

Area; Graph drawing; Grid; Orthogonal drawing; Planar drawing; Straight line drawing; Tree; Upward drawing

Indexed keywords

EID: 0030496765     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195996000228     Document Type: Article

References (32)

1. S. Bhatt and S. Cosmadakis. The complexity of minimizing wire lengths in VLSI layouts. Inform. Process. Lett., 25:263-267, 1987.
2. S. N. Bhatt and F. T. Leighton. -A framework for solving VLSI graph layout problems. J. Comput. Syst. Sci., 28:300-343, 1984.
3. F. J. Brandenburg. Nice drawings of graphs and trees are computationally hard. Technical Report MIP-8820, Fakultat fur Mathematik und Informatik, Univ. Passau, 1988.
4. R. P. Brent and H. T. Kung. On the area of binary tree layouts. Inform. Process. Lett., 11:521-534, 1980.
5. B. Chazelle. A theorem on polygon cutting with applications. In Proc. 23rd Annu. IEEE Sympos. Found. Comput. Sci., pages 339-349, 1982.
6. R. F. Cohen, G. Di Battista, R. Tamassia, I. G. Tollis, and P. Bertolassi. A framework for dynamic graph drawing. In Proc. 8th Annu. ACM Sympos. Comput. Geom., pages 261-270, 1992.
7. P. Crescenzi, G. Di Battista, and A. Piperno. A note on optimal area algorithms for upward drawings of binary trees. Comput. Geom. Theory Appl., 2:187-200, 1992.
8. P. Crescenzi and A. Piperno. Optimal-area upward drawings of AVL trees. In R. Tamassia and I. G. Tollis, editors, Graph Drawing (Proc. GD '94), volume 894 of Lecture Notes in Computer Science, pages 307-317. Springer-Verlag, 1995.
9. 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.
10. 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.
11. 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.
12. 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.
13. P. Eades, T. Lin, and X. Lin. Two tree drawing conventions. Technical Report 174, Department of Computer Science, University of Queensland, 1990. to appear in Comput. Geom. Theory Appl.
14. P. Eades, T. Lin, and X. Lin. Minimum size h-v drawings. In Advanced Visual Interfaces (Proceedings of AVI '92), volume 36 of World Scientific Series in Computer Science, pages 386-394, 1992.
15. 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.
16. M. Fürer, X. He, M.-Y. Kao, and B. Raghavachari. O(n log n)-work parallel algorithm for straight-line grid embedding of planar graphs. In Proc. ACM Sympos. Parallel Algorithms Architect., pages 100-109, 1992.
17. L. J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. E. Tarjan. Lineartime algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica, 2:209-233, 1987.
18. G. Kant. Drawing planar graphs using the canonical ordering. Algorithmica (special issue on Graph Drawing, edited by G. Di Battista and R. Tamassia). To appear.
19. G. Kant, G. Liotta, R. Tamassia, and I. Tollis. Area requirement of visibility representations of trees. In Proc. 5th Canad. Conf. Comput. Geom., pages 192-197, Waterloo, Canada, 1993.
20. C. E. Leiserson. Area-efficient graph layouts (for VLSI). In Proc. 21st Annu. IEEE Sympos. Found. Comput. Sci., pages 270-281, 1980.
21. S. Malitz and A. Papakostas. On the angular resolution of planar graphs. SIAM J. Discrete Math., 7:172-183, 1994.
22. J. O'Rourke. Computational geometry column 18. Internat. J. Comput. Geom. Appl., 3:107-113, 1993. Also in SIGACT News 24:1 (1993), 20-25.
23. J. O'Rourke. Computational geometry column 18. Internat. J. Comput. Geom. Appl., 3:107-113, 1993. Also in SIGACT News 24:1 (1993), 20-25.
24. E. Reingold and J. Tilford. Tidier drawing of trees. IEEE Trans. Softw. Eng., SE-7(2):223-228, 1981.
25. P. Rosenstiehl and R. E. Tarjan. Rectilinear planar layouts and bipolar orientations of planar graphs. Discrete Comput. Geom., l(4):343-353, 1986.
26. W. Schnyder. Embedding planar graphs on the grid. In Proc. 21st ACM-SIAM Sympos. Discrete Algorithms, pages 138-148, 1990.
27. Y. Shiloach. Arrangements of Planar Graphs on the Planar Lattice. PhD thesis, Weizmann Institute of Science, 1976.
28. K. J. Supowit and E. M Reingold. The complexity of drawing trees nicely. Acta Inform., 18:377-392, 1983.
29. R. Tamassia and I. G. Tollis. A unified approach to visibility representations of planar graphs. Discrete Comput. Geom., 1(4):321-341, 1986.
30. R, Tamassia and I. G. Tollis, editors. Graph Drawing (Proc. GD '94), volume 894 of Lecture Notes in Computer Science. Springer-Verlag, 1995.
31. W. T. Tutte. How to draw a graph. Proceedings London Mathematical Society, 13(3):743-768, 1963.
32. L. Valiant. Universality considerations in VLSI circuits. IEEE Trans. Comput., C-30(2):135-140, 1981.