Rectangle visibility graphs: Characterization, construction, and compaction

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2607, Issue , 2003, Pages 26-37

  Streinu, Ileana ^a   Whitesides, Sue ^b  

^a SMITH COLLEGE   (United States)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPACTION; POLYNOMIAL APPROXIMATION; TOPOLOGY; VISIBILITY;

ASSOCIATED GRAPH; BOUNDING BOX; COMPACT SETS; NP COMPLETE; OPTIMUM LENGTH; POLYNOMIAL-TIME ALGORITHMS; VERTICAL DIRECTION; VISIBILITY GRAPHS;

GEOMETRY;

EID: 33645614575     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36494-3_4     Document Type: Article

References (28)

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), vol. 1027 of Lecture Notes Comput. Sci., pp. 8-19. Springer-Verlag, 1996.
2. G. Brightwell and P. Winkler. Counting linear extensions is #P-complete. Proc. STOC 23, pp. 175-181, 1991.
3. K.S. Booth and G.S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput.System Sci. 13, pp. 335-379, 1976.
4. P. Bose, A. Dean, J. Hutchinson, and T. Shermer. On rectangle visibility graphs I: k-trees and caterpillar forests. Tech. report, DIMACS and Simon Fraser U., May 1996.
5. 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. In D. Avis and P. Bose, eds., Snapshots in Computational and Discrete Geometry, Vol. III, pp. 2-25. McGill U., July 1994. McGill tech. report SOCS-94.50.
6. P. Bose, H. Everett, Michael E. Houle, S. Fekete, A. Lubiw, H. Meijer, K. Romanik, G. Rote, T. Shermer, S. Whitesides, and Christian Zelle. A visibility representation for graphs in three dimensions. J. Graph Algorithms and Applications, vol. 2, no. 3, pp. 1-16, 1998.
7. 42 is a box visibility graph. In Snapshots of Computational and Discrete Geometry, vol. 3, pp. 88-91. School Comput. Sci., McGill U., Montreal, July 1994. Tech. report SOCS-94.50.
8. A. M. Dean and J. P. Hutchinson. Rectangle-visibility representations of bipartite graphs. In R. Tamassia and I. G. Tollis, eds., Graph Drawing (Proc. GD '94), vol. 894 of Lecture Notes Comput. Sci., pp. 159-166. Springer-Verlag, 1995.
9. G. Di Battista, P. Eades, R. Tamassia, and I. Tollis. Graph Drawing: Algorithms for the visualization of graphs. Prentice Hall, Upper Saddle River NJ, 1999.
10. Jeong-In Doh and Kyung-Yong Chwa. Visibility problems for orthogonal objects in two or three dimensions. Visual Comput., vol. 4, no. 2, pp. 84-97, July 1988.
11. S. P. Fekete, M. E. Houle, and S. Whitesides. New results on a visibility representation of graphs in 3-d. In F. Brandenburg, ed., Graph Drawing '95, vol. 1027 of Lecture Notes Comput. Sci., pp. 234-241. Springer-Verlag, 1996.
12. H. de Praysseix and P. Rosenstiehl. L'algorithme gauche-droite pour le plongement des graphes dans le plan.
13. Xin He and Ming-Yang Kao. Regular edge labelings and drawings of planar graphs. In Proc. Graph Drawing conf., pp. 96-103, 1994.
14. J. Hopcroft and R. Tarjan. Efficient planarity testing. J. Assoc. Comput. Machin. 21, pp. 549-568, 1974.
15. J. P. Hutchinson, T. Shermer, and A. Vince. On representations of some thickness-two graphs. In F. Brandenburg, ed., Graph Drawing '95, vol. 1027 of Lecture Notes Comput. Sci., pp. 324-332. Springer-Verlag, 1995.
16. A. Josefczyk, J. Miller, and J. O'Rourke. Arkin's conjecture for rectangle and box visibility graphs. Tech. Report 036, Dept. Comput. Sci., Smith College, July 1994.
17. D. G. Kirkpatrick and S. K. Wismath. Weighted visibility graphs of bars and related flow problems. In Proc. 1st Workshop Algorithms Data Struct., vol. 382 of Lecture Notes Comput. Sci., pp. 325-334. Springer-Verlag, 1989.
18. A. Lempel, S. Even and I. Cederbaum. An algorithm for planarity testing of graphs. In (P. Rosenstiehl, ed., Theory of Graphs (Int. Symposium, Rome, 1966), pp. 215-232, Gordon and Breach, New York, 1967.
19. E. Lodi and L. Pagli. A VLSI solution to the vertical segment visibility problem. IEEE Trans. Comput., vol. C-35, no. 10, pp. 923-928, 1986.
20. F. Luccio, S. Mazzone, and C. Wong. A note on visibility graphs. Discrete Math., vol. 64, pp. 209-219, 1987.
21. M. H. Overmars and D. Wood. On rectangular visibility. J. Algorithms, vol. 9, pp. 372-390, 1988.
22. K. Romanik. Directed rectangle-visibility graphs have unbounded dimension. In Proc. 7th Canad. Conf. Comput. Geom., pp. 163-167, 1995.
23. Pierre Rosenstiehl and Robert Tarjan. Rectiliniar planar layouts and bipolar orientations of planar graphs. Discrete Comput Geom., vol. 1, pp. 343-353, 1986.
24. T. Shermer. On rectangle visibility graphs III: External visibility and complexity. Tech. report, DIMACS and Simon Fraser U., April 1996.
25. T. C. Shermer. On rectangle visibility graphs, III: External visibility and complexity. In Proc. 8th Canad. Conf. Comput. Geom., pp. 234-239, 1996.
26. R. Tamassia and I. G. Tollis. A unified approach to visibility representations of planar graphs. Discrete Comput. Geom., vol. 1, no. 4, pp. 321-341, 1986.
27. S. K. Wismath. Characterizing bar line-of-sight graphs. In Proc. 1st Annu. ACM Sympos. Comput. Geom., pp. 147-152, 1985.
28. S. K. Wismath. Bar-Representable Visibility Graphs and Related Flow Problems. Ph.D. thesis, Dept. Comput. Sci., U. British Columbia, 1989.