Rectangle and box visibility graphs in 3D

International Journal of Computational Geometry and Applications

Volumn 9, Issue 1, 1999, Pages 1-27

  Fekete, Sándor P ^a   Meijer, Henk ^b  

^a UNIVERSITY OF COLOGNE   (Germany)

^b QUEEN S UNIVERSITY   (Canada)

Author keywords

3 dimensional geometry; Graph drawing; Graph representation; Orthogonal objects; Visibility

Indexed keywords

EID: 0033484513     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195999000029     Document Type: Article

References (20)

1. H. Alt, M. Godau and S. Whitesides, "Universal 3-dimensional visibility representations for graphs," Proc. Graph Drawing 95, Passau 1996, Lecture Notes in Computer Science # 1027, Springer-Verlag, 1996, pp. 8-19.
2. P. Bose, H. Everett, S. P. Fekete, A. Lubiw, H. Meijer, K. Romanik, T. Shermer, and S. Whitesides, "On a visibility representation for graphs in three dimensions," Proc. Graph Drawing '93, Paris (Sèvres), 1993, pp. 38-39.
3. P. Bose, H. Everett, S. P. Fekete, A. Lubiw, H. Meijer, K. Romanik, T. Shermer, and S. Whitesides, "On a visibility representation for graphs in three dimensions," Snapshots of Computational and Discrete Geometry, 3, eds. D. Avis and P. Bose, McGill University School of Computer Science Technical Report SOCS-94.50, July 1994, pp. 2-25.
4. P. Bose, H. Everett, S. P. Fekete, A. Lubiw, H. Meijer, K. Romanik, T. Shermer, and S. Whitesides, "On a visibility representation for graphs in three dimensions," ZPR Technical Report 95-205, available via http://vww.zpr.uni-koeln.de.
5. 42 is a box visibility graph," Tech. Report #034, Smith College, 1994.
6. F.J. Cobos, J.C. Dana, F. Hurtado, A. Marquez, and F. Mateos, "On a visibility representation of graphs," Proc. Graph Drawing 95, Passau 1996, Lecture Notes in Computer Science #1072, Springer-Verlag 1996, pp. 152-161.
7. R. Cohen, P. Eades, T. Lin, and F. Ruskey, "Three-dimensional graph drawing," Proc. Graph Drawing '94, Princeton NJ, 1994. Lecture Notes in Computer Science #894, Springer-Verlag, 1995, pp. 1-11.
8. A. Dean and J. Hutchison, "Rectangle visibility representations of bipartite graphs," Proc. Graph Drawing '94, Princeton NJ, 1994, Lecture Notes in Computer Science #894, Springer-Verlag, 1995, pp. 159-166.
9. S. P. Fekete, M. E. Houle, and S. Whitesides, "New results on a visibility representation of graphs in 3D," Proc. Graph Drawing 95, Passau 1996, Lecture Notes in Computer Science #1072, Springer-Verlag 1996, pp. 234-241.
10. S. P. Fekete, J. Schepers, and M. Wottawa, "A practical insertion heuristic for 3-dimensional packing problems," Manuscript.
11. P. Hall, "On representatives of subsets," J. London Math. Soc., 10, 1935, pp. 26-30.
12. J. Hutchinson, T. Shermer, and A. Vince, "On representations of some thickness-two graphs," Proc. Graph Drawing 95, Passau 1996, Lecture Notes in Computer Science #1072, Springer-Verlag 1996, pp. 324-332.
13. H. Koike, "An application of three-dimensional visualization to object-oriented programming," Proc. of Advanced Visual Interfaces AVI '92, Rome, May 1992, v. 36 of World Scientific Series in Computer Science, 1992, pp. 180-192.
14. E. Kranakis, D. Krizanc, and J. Urrutia, "On the number of directions in visibility representations of graphs," Proc. Graph Drawing '94, Princeton NJ, 1994, Lecture Notes in Computer Science #894, Springer-Verlag, 1995, pp. 167-176.
15. J. Mackinley, G. Robertson, and S. Card, "Cone trees: animated 3d visualizations of hierarchical information," Proc. of the SIGCHI Conf. on Human Factors in Computing, 1991, pp. 189-194.
16. K. Romanik, "Directed VR-representable graphs have unbounded dimension," Proc. Graph Drawing '94, Princeton, NJ, 1994, Lecture Notes in Computer Science #894, Springer-Verlag, 1995, pp. 177-181.
17. G. Rote and C. Zelle, Personal communication, 1996.
18. R. Tamassia and I.G. Tollis, "A unified approach to visibility representations of planar graphs," Discrete Comput. Geom., 1, 1986, pp. 321-341.
19. S. K. Wismath, "Characterizing bar line-of-sight graphs," Proc. ACM Symp. on Computational Geometry, 1985, pp. 147-152.
20. M. Wottawa, "Struktur und algorithmische Behandlung von praxisorientierten dreidimensionalen Packungsproblemen," Doctoral Thesis, Mathematisches Institut, Universität zu Köln, 1996.