Lombardi drawings of graphs

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

Volumn 6502 LNCS, Issue , 2011, Pages 195-207

  Duncan, Christian A ^a   Eppstein, David ^b   Goodrich, Michael T ^b   Kobourov, Stephen G ^c   Nöllenburg, Martin ^b  

^a Louisiana Tech University   (United States)

^b Irvine   (United States)

^c University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANGULAR RESOLUTION; CIRCULAR ARC; GRAPH DRAWING; LINE SEGMENT; PLANAR GRAPH; POLYLINES; REGULAR GRAPHS;

DRAWING (GRAPHICS); GRAPH THEORY;

GRAPH THEORY; GRAPHIC METHODS;

EID: 79952270419     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-18469-7_18     Document Type: Conference Paper

References (31)

1. Aichholzer, O., Aigner, W., Aurenhammer, F., Dobiáš ová, K. Č., Jüttler, B.: Arc triangulations. In: Proc. 26th Eur. Worksh. Comp. Geometry (EuroCG 2010), Dortmund, Germany, pp. 17-20 (2010)
2. Alon, N.: A simple algorithm for edge-coloring bipartite multigraphs. Information Processing Letters 85(6), 301-302 (2003), doi:10.1016/S0020-0190(02) 00446-5
3. Baur, M., Brandes, U.: Crossing reduction in circular layouts. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 332-343. Springer, Heidelberg (2004), http://www.springerlink.com/content/ fepu2a3hd195ffjg/
4. Biedl, T.C., Bose, P., Demaine, E.D., Lubiw, A.: Efficient algorithms for Petersen's matching theorem. J. Algorithms 38(1), 110 (2001), doi:10.1006/jagm.2000.1132
5. Brandes, U., Schlieper, B.: Angle and distance constraints on tree drawings. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 54-65. Springer, Heidelberg (2007), doi:10.1007/978-3-540-70904-6 7
6. Brandes, U., Shubina, G., Tamassia, R.: Improving angular resolution in visualizations of geographic networks. In: Data Visualization 2000. Proc. 2nd Eurographics/IEEE TCVG Symp. Visualization (VisSym 2000), pp. 23-32. Springer, Heidelberg (2000)
7. Brandes, U., Wagner, D.: Using graph layout to visualize train interconnection data. J. Graph Algorithms Appl. 4(3), 135-155 (2000)
8. Cheng, C.C., Duncan, C.A., Goodrich, M.T., Kobourov, S.G.: Drawing planar graphs with circular arcs. Discrete Comput. Geom. 25(3), 405-418 (2001), doi:10.1007/s004540010080
9. Cole, R., Ost, K., Schirra, S.: Edge-coloring bipartite multigraphs in O(ElogD) time. Combinatorica 21(1), 5-12 (2001), doi:10.1007/s004930170002
10. di Battista, G., Vismara, L.: Angles of planar triangular graphs. SIAM J. Discrete Math. 9(3), 349 (1996), doi:10.1137/S0895480194264010
11. Duncan, C.A., Eppstein, D., Goodrich, M.T., Kobourov, S.G., Nöllenburg, M.: Lombardi Drawings of Graphs. (September 2010) ArXiv e-prints, arXiv:1009.0579
12. Duncan, C.A., Eppstein, D., Goodrich, M.T., Kobourov, S.G., Nöllenburg, M.: Drawing trees with perfect angular resolution and polynomial area. In: Proc. 18th Int. Symp. on Graph Drawing (GD 2010), Springer, Heidelberg (2010)
13. Efrat, A., Erten, C., Kobourov, S.G.: Fixed-location circular arc drawing of planar graphs. J. Graph Algorithms Appl. 11(1), 145-164 (2007), http://jgaa.info/accepted/2007/EfratErtenKobourov2007.11.1.pdf
14. Finkel, B., Tamassia, R.: Curvilinear graph drawing using the force-directed method. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 448-453. Springer, Heidelberg (2005), doi:10.1007/978-3-540-31843-9 46
15. Gabow, H.N.: Using Euler partitions to edge color bipartite multigraphs. Int. J. Parallel Programming 5(4), 345-355 (1976), doi:10.1007/BF00998632
16. Gansner, E.R., Koren, Y.: Improved circular layouts. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 386-398. Springer, Heidelberg (2007), doi:10.1007/978-3-540-70904-6 37
17. Garg, A., Tamassia, R.: Planar drawings and angular resolution: algorithms and bounds. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 12-23. Springer, Heidelberg (1994), doi:10.1007/BFb0049393
18. Gutwenger, C., Mutzel, P.: Planar polyline drawings with good angular resolution. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 167-182. Springer, Heidelberg (1999), doi:10.1007/3-540-37623-2 13
19. Halin, R.: Über simpliziale Zerfällungen beliebiger (endlicher oder unendlicher) Graphen. Math. Ann. 156(3), 216-225 (1964), doi:10.1007/BF01363288
20. Holm, J., de Lichtenberg, K., Thorup, M.: Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM48(4), 723-760 (2001), doi:10.1145/502090.502095
21. Kant, G.: Drawing planar graphs using the canonical ordering. Algorithmica 16, 4-32 (1996), doi:10.1007/BF02086606
22. Kocombining double acute accentnig, D.: Gráfok és mátrixok. Matematikai és Fizikai Lapok 38, 116-119 (1931)
23. Lick, D.R., White, A.T.: K-degenerate graphs. Canad. J. Math. 22, 1082-1096 (1970), http://www.smc.math.ca/cjm/v22/p1082
24. Lombardi, M., Hobbs, R.: Mark Lombardi: Global Networks. Independent Curators (2003)
25. Malitz, S., Papakostas, A.: On the angular resolution of planar graphs. SIAM J. Discrete Math. 7(2), 172-183 (1994), doi:10.1137/S0895480193242931
26. Morgan, F.: Soap bubbles in R2 and in surfaces. Pacific J. Math. 165(2), 347-361 (1994), http://projecteuclid.org/euclid.pjm/1102621620
27. Mulder, H.M.: Julius Petersen's theory of regular graphs. Discrete Mathematics 100(1-3), 157-175 (1992), doi:10.1016/0012-365X(92)90639-W
28. Petersen, J.: Die Theorie der regulären Graphs. Acta Math. 15(1), 193-220 (1891), doi:10.1007/BF02392606
29. Schrijver, A.: Bipartite edge coloring in O(Δm) time. SIAM J. Comput. 28(3), 841-846 (1999), doi:10.1137/S0097539796299266
30. Six, J.M., Tollis, I.G.: A framework for circular drawings of networks. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 107-116. Springer, Heidelberg (1999)
31. Thorup, M.: Near-optimal fully-dynamic graph connectivity. In: Proc. 32nd ACM Symp. Theory of Computing (STOC 2000), pp. 343-350 (2000), doi:10.1145/335305.335345