Edge-weighted contact representations of planar graphs

Journal of Graph Algorithms and Applications

Volumn 17, Issue 4, 2013, Pages 441-473

  Nöllenburg, Martin ^a   Prutkin, Roman ^a   Rutter, Ignaz ^a  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; GRAPHIC METHODS;

CONTACT LENGTH; EDGE WEIGHTS; LINEAR TIME; LOW BOUND; LOWER AND UPPER BOUNDS; NP COMPLETE; OUTERPLANAR GRAPH; PLANAR GRAPH; REGULAR EDGE LABELING; WEIGHTED PLANAR GRAPHS;

GRAPH THEORY;

EID: 84880723451     PISSN: 15261719     EISSN: None     Source Type: Journal    
DOI: 10.7155/jgaa.00299     Document Type: Article

References (26)

1. M. J. Alam, T. Biedl, S. Felsner, A. Gerasch, M. Kaufmann, and S. G. Kobourov. Linear-time algorithms for proportional contact graph representations. In Proc. 22nd International Symposium on Algorithms and Computation (ISAAC'11), volume 7074 of Lecture Notes Comput. Sci., pages 281-291. Springer-Verlag, 2011. doi:10.1007/978-3-642-25591-5_30.
2. M. J. Alam, T. Biedl, S. Felsner, M. Kaufmann, S. G. Kobourov, and T. Ueckerdt. Computing cartograms with optimal complexity. In Proc. 28th ACM Symposium on Computational Geometry (SoCG'12), pages 21-30. ACM, 2012. doi:10. 1145/2261250.2261254.
3. T. Biedl and B. Genc. Complexity of octagonal and rectangular cartograms. In Proc. 17th Canadian Conference on Computational Geometry (CCCG'05), pages 117-120, 2005.
4. T. Biedl and L. E. R. Velázquez. Orthogonal cartograms with few corners per face. In Proc. 12th International Symposium on Algorithms and Data Structures (WADS'11), volume 6844 of Lecture Notes Comput. Sci., pages 98-109. Springer-Verlag, 2011. doi:10.1007/978-3-642-22300-6_9.
5. S. Cabello, E. D. Demaine, and G. Rote. Planar embeddings of graphs with specified edge lengths. J. Graph Algorithms Appl., 11(1):259-276, 2007. doi: 10.7155/jgaa.00145.
6. J. Chalopin and D. Gonçalves. Every planar graph is the intersection graph of segments in the plane. In Proc. 41st Annual ACM Symposium on Theory of Computing (STOC'09), pages 631-638. ACM, 2009. doi:10.1145/1536414.1536500.
7. M. de Berg, E. Mumford, and B. Speckmann. On rectilinear duals for vertexweighted plane graphs. Discrete Mathematics, 309(7):1794-1812, 2009. doi: 10.1016/j.disc.2007.12.087.
8. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, 1999.
9. P. Eades and N. C. Wormald. Fixed edge-length graph drawing is NP-hard. Discrete Applied Mathematics, 28(2):111-134, 1990. doi:10.1016/0166-218X(90) 90110-X.
10. D. Eppstein, E. Mumford, B. Speckmann, and K. Verbeek. Area-universal and constrained rectangular layouts. SIAM J. Comput., 41(3):537-564, 2012. doi: 10.1137/110834032.
11. É. Fusy. Transversal structures on triangulations: A combinatorial study and straight-line drawings. Discrete Math., 309(7):1870-1894, 2009. doi:10.1016/ j.disc.2007.12.093.
12. X. He. On finding the rectangular duals of planar triangular graphs. SIAM J. Comput., 22(6):1218-1226, 1993. doi:10.1137/0222072.
13. P. Hliněný and J. Kratochvíl. Representing graphs by disks and balls (a survey of recognition-complexity results). Discrete Mathematics, 229(1-3):101-124, 2001. doi:10.1016/S0012-365X(00)00204-1.
14. Kawaguchi and H. Nagamochi. Orthogonal drawings for plane graphs with specified face areas. In Proc. Theory and Application of Models of Computation (TAMC'07), volume 4484 of Lecture Notes Comput. Sci., pages 584-594. Springer-Verlag, 2007. doi:10.1007/978-3-540-72504-6_53.
15. D. E. Knuth and A. Raghunathan. The problem of compatible representatives. SIAM J. Discrete Math., 5(3):422-427, 1992. doi:10.1137/0405033.
16. P. Koebe. Kontaktprobleme der konformen Abbildung. Ber. Sächs. Akad. Wiss. Leipzig, Math.-Phys. Klasse, 88:141-164, 1936.
17. K. A. Kozminski and E. Kinnen. Rectangular dualization and rectangular dissections. IEEE Trans. Circuits and Systems, 35(11):1401-1416, 1988. doi: 10.1109/31.14464.
18. S. M. Leinwand and Y.-T. Lai. An algorithm for building rectangular floor-plans. In Proc. 21st Design Automation Conference, pages 663-664, 1984.
19. C.-C. Liao, H.-I. Lu, and H.-C. Yen. Compact floor-planning via orderly spanning trees. J. Algorithms, 48(2):441-451, 2003. doi:10.1016/S0196-6774(03) 00057-9.
20. D. Lichtenstein. Planar formulae and their uses. SIAM J. Comput., 11(2):329-343, 1982. doi:10.1137/0211025.
21. T. A. McKee and F. R. McMorris. Topics in Intersection Graph Theory. SIAM, 1999.
22. T. Nishizeki and M. S. Rahman. Rectangular drawing algorithms. In R. Tamassia, editor, Handbook of Graph Drawing and Visualization, chapter 13. CRC Press, 2012. To appear.
23. R. Prutkin. Kontaktrepräsentationen von kantengewichteten planaren Graphen. Diploma thesis, Karlsruhe Institute of Technology, 2012.
24. R. Tamassia. Drawing algorithms for planar st-graphs. Australasian J. Combinatorics, 2:217-235, 1990.
25. M. van Kreveld and B. Speckmann. On rectangular cartograms. Comput. Geom. Theory Appl., 37(3):175-187, 2007. doi:10.1016/j.comgeo.2006.06.002.
26. K.-H. Yeap and M. Sarrafzadeh. Floor-planning by graph dualization: 2-concave rectilinear modules. SIAM J. Comput., 22(3):500-526, 1993. doi:10.1137/ 0222035.