An application of well-orderly trees in graph drawing

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

Volumn 3843 LNCS, Issue , 2006, Pages 458-467

  Zhang, Huaming ^a   He, Xin ^b  

^a University of Alabama in Huntsville   (United States)

^b State University of New York   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; GRAPH THEORY; IMAGE CODING; INFORMATION TECHNOLOGY; STATISTICAL METHODS; TREES (MATHEMATICS);

GRAPH ENCODING; GRAPH ENUMERATION; GRAPH GENERATION; VISIBILITY REPRESENTATION;

DRAWING (GRAPHICS);

EID: 33745679616     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11618058_41     Document Type: Conference Paper

References (26)

1. G. di Battista, P. Eades, R. Tammassia, and I. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Princeton Hall, 1998
2. N. Bonichon, B. Le Saëc and M. Mosbah, Wagner's theorem on realizers, in: Proc. ICALP'02, Lecture Notes in Computer Science, Vol. 2380, (Springer, Berlin, 2002) 1043-1053.
3. N. Bonichon, C. Gavoille, and N. Hanusse, An information-theoretic upper bound of planar graphs using triangulation, in Proc. STACS'03, pp 499-510, Lectures Notes in Computer Science, Vol. 2607, Springer-Verlag, 2003.
4. N. Bonichon, C. Gavoille, and N. Hanusse, Canonical decomposition of outerplanar maps and application to enumeration, coding and generation, In Proc. WG'2003, pp. 81-92, Lecture Notes in Computer Science, Vol. 2880, Springer-Verlag, 2003
5. H.-L. Chen, C.-C. Liao, H.-I. Lu and H.-C. Yen, Some applications of orderly spanning trees in graph drawing, in Proc. Graph Drawing'02, pp. 332-343, Lecture Notes in Computer Science, Vol. 2528, Springer-Verlag, Berlin, 2002.
6. Y.-T. Chiang, C.-C. Lin and H.-I. Lu, Orderly spanning trees with applications to graph encoding and graph drawing, in Proc. of the 12th Annual ACM-SIAM SODA, pp. 506-515, ACM Press, New York, 2001.
7. M. Chrobak and G. Kant, Convex grid drawings of 3-connected planar graphs, Technical Report RUU-CS-93-45, Department of Computer Science, Utrecht University, Holland, 1993.
8. U. Fößmeier, G. Kant and M. Kaufmann, 2-Visibility drawings of planar graphs, in Proc. 4th International Symposium on Graph Drawing, pp. 155-168, Lecture Notes in Computer Science, Vol. 1190, Springer-Verlag, Berlin, 1996.
9. H. de Praysseix, J. Pach and R. Pollack, How to draw a planar graph on a grid. Combinatorica 10 (1990), 41-51.
10. G. Kant, Drawing planar graphs using the lmc-ordering, in Proc. 33rd Symposium on Foundations of Computer Science, pp.101-110, IEEE, Pittsburgh, 1992.
11. G. Kant, Algorithms for drawing planar graphs, Ph.D. Dissertation, Department of Computer Science, University of Utrecht, Holland, 1993.
12. G. Kant, Drawing planar graphs using the canonical ordering, Algorithmica 16 (1996), 4-32.
13. G. Kant, A more compact visibility representation. International Journal of Computational Geometry and Applications 7 (1997), 197-210.
14. G. Kant and X. He, Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems. Theoretical Computer Science 172 (1997), 175-193.
15. A. Lempel, S. Even and I. Cederbaum, An algorithm for planarity testing of graphs, in Theory of Graphs (Proc. of an International Symposium, Rome, July 1966), pp. 215-232, Rome, 1967.
16. C.-C. Liao, H.-I. Lu and H.-C. Yen, Floor-planning via orderly spanning trees, in Proc. 9th International Symposium on Graph Drawing, pp. 367-377, Lecture Notes in Computer Science, Vol. 2265, Springer-Verlag, Berlin, 2002.
17. C.-C. Lin, H.-I. Lu and I-F. Sun, Improved compact visibility representation of planar graph via Schnyder's realizer, in: SIAM Journal on Discrete Mathematics, 18 (2004), 19-29.
18. P. Ossona de Mendez, Orientations bipolaires. PhD thesis, Ecole des Hautes Etudes en Sciences Sociales, Paris, 1994.
19. P. Rosenstiehl and R. E. Tarjan, Rectilinear planar layouts and bipolar orientations of planar graphs. Discrete Comput. Geom. 1 (1986), 343-353.
20. W. Schnyder, Planar graphs and poset dimension. Order 5 (1989), 323-343.
21. W. Schnyder, Embedding planar graphs on the grid, in Proc. of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 138-148, SIAM, Philadelphia, 1990.
22. R. Tamassia and I.G.Tollis, An unified approach to visibility representations of planar graphs. Discrete Comput. Geom. 1 (1986), 321-341.
23. H. Zhang and X. He, Compact Visibility Representation and Straight-Line Grid Embedding of Plane Graphs, in: Proc. WADS'03, Lecture Notes in Computer Science, Vol. 2748, (Springer-Verlag Heidelberg, 2003) 493-504.
24. H. Zhang and X. He, On Visibility Representation of Plane Graphs, in; Proc. STAGS'04, Lecture Notes in Computer Science, Vol. 2996, (Springer-Verlag Heidelberg, 2004) 477-488.
25. H. Zhang and X. He, New Theoretical Bounds of Visibility Representation of Plane Graphs, in: Proc. GD'2004, Lecture Notes in Computer Science, Vol. 3383, (Springer-Verlag, 2005) pp. 425-430.
26. H. Zhang and X. He, Improved Visibility Representation of Plane Graphs, Discrete Comput. Geom. 30 (2005), 29-29.