1 BALLOON-LAYOUT . . . 14
2 RADIAL-LAYOUT . . . 20
3 SPREADING . . . 29
4 CIRCLE-LAYOUT . . . 33
5 CONFLICT COMPUTATION . . . 97
6 PATH-BASED TREE SUPPORT . . . 100
Bibliography
Bachmaier, C., Brandes, U., Schlieper, B., 2005. Drawing phylogenetic trees.
In: Deng, X., Du, D.-Z. (Eds.), Proceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC ’05). Vol. 3827 of Lec-ture Notes in Computer Science. Springer, pp. 1110–1121. II, 22
Beeri, C., Fagin, R., Maier, D., Yannakakis, M., 1983. On the desirability of acyclic database schemes. Journal of the Association for Computing Machinery 30 (4), 479–513. 87
B¨ohringer, K.-F., Paulisch, F. N., 1990. Using constraints to achieve stability in automatic graph layout algorithms. In: Proceedings of the ACM Human Factors in Computing Systems Conference (CHI ’90). ACM, The Association for Computing Machinery, pp. 43–51. 55
Brandes, U., Cornelsen, S., Pampel, B., Sallaberry, A., 2010a. Blocks of hyper-graphs. In: Tischler and Radzik (2010), pp. 201–211. 87, 88
Brandes, U., Cornelsen, S., Pampel, B., Sallaberry, A., 2010b. Path-based sup-ports for hypergraphs. In: Tischler and Radzik (2010), pp. 20–33, invited journal version submitted to Journal of Discrete Algorithms. II
Brandes, U., Pampel, B., 2009. On the hardness of orthogonal-order preserving graph drawing. In: Tollis and Patrignani (2009), pp. 266–277, extended version submitted to Journal of Graph Algorithms and Applications. II
Brandes, U., Schlieper, B., 2009. Angle and distance constraints on tree drawing.
In: Tollis and Patrignani (2009), pp. 54–65. II
Brandes, U., Shubina, G., Tamassia, R., 2000. Improving angular resolution in visualizations of geographic networks. In: de Leeuw, W., van Liere, R. (Eds.), Data Visualization 2000. Proceedings of the 2nd Joint Eurographics and IEEE TCVG Symposium on Visualization (VisSym ’00). Springer, pp. 23–33. 39, 43
Brass, P., Cenek, E., Duncan, C. A., Efrat, A., Erten, C., Ismailescu, D. P., Kobourov, S. G., Lubiw, A., Mitchell, J. S. B., 2003. On simultaneous planar graph embeddings. In: Dehne, F., Sack, J.-R., Smid, M. H. M. (Eds.), Pro-ceedings of the 8th Workshop on Algorithms and Data Structures (WADS ’03).
Vol. 2748 of Lecture Notes in Computer Science. Springer, pp. 243–255. 71 Bridgeman, S., Tamassia, R., 1998. Difference metrics for interactive orthogonal
graph drawing algorithms. In: Whitesides (1998), pp. 57–71. 55
Bridgeman, S., Tamassia, R., 2002. A user study in similarity measures for graph drawing. Journal of Graph Algorithms and Applications 6 (3), 225–254. 55 Buchin, K., van Kreveld, M., Meijer, H., Speckmann, B., Verbeek, K., 2010.
On planar supports for hypergraphs. In: Eppstein and Gansner (2010), pp.
345–456. 87, 88, 94, 95, 99, 106
Bujt´as, C., Tuza, Z., 2009. Color-bounded hypergraphs, II: Interval hypergraphs and hypertrees. Discrete Mathematics 309 (22), 6391–6401. 87
Carlson, J., Eppstein, D., 2007. Trees with convex faces and optimal angles. In:
Kaufmann and Wagner (2007), pp. 77–88. 23
Carrizo, S. F., 2004. Phylogenetic trees: An information visualization perspec-tive. In: Chen, Y.-P. P. (Ed.), Asia-Pacific Bioinformatics Conference (APBC 2004). Vol. 29 of CRPIT. Australian Computer Society, pp. 315–320. 16 Chazelle, B., 1991. Triangulating a simple polygon in linear time. Discrete and
Computational Geometry 6 (5), 485–524. 38
Cheng, C. C., Duncan, C. A., Goodrich, M. T., Kobourov, S. G., 1999. Draw-ing planar graphs with circular arcs. In: Kratochv´ıl, J. (Ed.), ProceedDraw-ings of the 7th International Symposium on Graph Drawing (GD ’99). Vol. 1731 of Lecture Notes in Computer Science. Springer, pp. 117–126. 39
Delling, D., Gemsa, A., N¨ollenburg, M., Pajor, T., 2010. Path schematization for route sketches. In: Algorithm Theory - SWAT 2010. Vol. 6139 of Lecture Notes in Computer Science. Springer, pp. 285–296. 56
Di Battista, G., Eades, P., Tamassia, R., Tollis, I. G., 1994. Algorithms for drawing graphs: An annotated bibliography. Computational Geometry: The-ory and Applications 4, 235–282. 1
Di Battista, G., Eades, P., Tamassia, R., Tollis, I. G., 1999. Graph Drawing:
Algorithms for the Visualization of Graphs. Prentice Hall. 1
Douglas, D. H., Peucker, T. K., 1973. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. The Canadian Cartographer 10 (2), 112–122. 55
Duncan, C. A., Eppstein, D., Goodrich, M. T., Kobourov, S. G., N¨ollenburg, M., 2011. Drawing trees with perfect angular resolution and polynomial area.
In: Brandes, U., Cornelsen, S. (Eds.), Proceedings of the 18th International Symposium on Graph Drawing (GD 2010). Vol. 6502 of Lecture Notes in Computer Science. Springer, pp. 183–194. 2
Dunn, M. E., Goldman, M. S., 1998. Age and drinking-related differences in the memory organization of alcohol expectances in 3rd-, 6th-, 9th-, and 12th-grade children. Journal of Consulting and Clinical Psychology 66 (3), 579–585. 4, 109
Dwyer, T., Koren, Y., Marriott, K., 2006. Stress majorization with orthogonal ordering constraints. In: Healy and Nikolov (2006), pp. 141–152. 3, 55, 109 Dwyer, T., Schreiber, F., 2004. Optimal leaf ordering for two and a half
dimen-sional phylogenetic tree visualization. In: Churcher, N., Churcher, C. (Eds.), Australasian Symposium on Information Visualisation (invis.au 2004). Vol. 35 of CRPIT. Australian Computer Society, pp. 109–115. 17, 109
Eades, P., 1992. Drawing free trees. Bulletin of the Institute for Combinatorics and its Applications 5, 10–36. 12
Eades, P., Wormald, N. C., 1990. Fixed edge-length graph drawing is np-hard.
Discrete Applied Mathematics 28, 111–134. 11, 19, 56
Eppstein, D., Gansner, E. R. (Eds.), 2010. Proceedings of the 17th International Symposium on Graph Drawing (GD 2009). Vol. 5849 of Lecture Notes in Computer Science. Springer. 114, 118
Felsenstein, J., 1973. Maximum likelihood and minimum-steps methods for esti-mating evolutionary trees from data on discrete characters. Systematic Zool-ogy 22, 240–249. 19
Felsenstein, J., 2004. Inferring Phylogenies. Sinauer Associates. 16, 22
Finkel, B., Tamassia, R., 2005. Curvilinear graph drawing using the force-directed method. In: Pach, J. (Ed.), Proceedings of the 12th International Symposium on Graph Drawing (GD ’04). Vol. 3383 of Lecture Notes in Com-puter Science. Springer, pp. 448–453. 39
Fitch, W. M., 1971. Toward defining the course of evolution: Minimum change for a specified tree topology. Systematic Zoology 20, 406–416. 19
Flower, J., Fish, A., Howse, J., 2008. Euler diagram generation. Journal on Visual Languages and Computing 19 (6), 675–694. 87
Gabriel, K. R., 1971. The biplot graphical display of matrices with application to principal component analysis. Biometrika 58 (3), 453–467. 71
Garey, M. R., Johnson, D. S., 1979. Computers and Intractability: A Guide to the Theory of N P–Completeness. W.H. Freeman & Co. 9, 10
Garg, A., 1995. On drawing angle graphs. In: Tamassia, R., Tollis, I. G.
(Eds.), Proceedings of the DIMACS International Workshop on Graph Draw-ing (GD ’94). Vol. 894 of Lecture Notes in Computer Science. SprDraw-inger, pp.
84–95. 11
Gortler, S. J., Thorston, D., 2006. Discrete one-forms on meshes and applications to 3d mesh parameterization. Journal of Computer Aided Geometric Design, CAGD 23 (2), 83–112. 32
Healy, P., Nikolov, N. S. (Eds.), 2006. Proceedings of the 13th International Sym-posium on Graph Drawing (GD ’05). Vol. 3843 of Lecture Notes in Computer Science. Springer. 115, 118
Heiser, W. J., de Leeuw, J., 1981. Multidimensional mapping of preference data.
Math´ematiques et sciences humaines 73, 39–96. 72
Imai, H., Iri, M., 1986. An optimal algorithm for approximating a piecewise linear function. Journal of Information Processing 9 (3), 159–162. 55
Johnson, D. S., Krishnan, S., Chhugani, J., Kumar, S., Venkatasubramanian, S., 2004. Compressing large boolean matrices using reordering techniques. In:
Nascimento, M. A., ¨Ozsu, M. T., Kossmann, D., Miller, R. J., Blakeley, J. A., Schiefer, K. B. (Eds.), Proceedings of the 30 th International Conference on Very Large Data Bases (VLDB ’04). Morgan Kaufman, pp. 13–23. 93
Johnson, D. S., Pollak, H. O., 1987. Hypergraph planarity and the complexity of drawing Venn diagrams. Journal of Graph Theory 11 (3), 309–325. 87, 94 Karp, R. M., 1972. Reducibility among combinatorial problems. In: Miller, R.,
Thatcher, J. (Eds.), Complexity of Computer Computations. Plenum Press, pp. 85–103. 94
Kaufmann, M., van Kreveld, M., Speckmann, B., 2009. Subdivision drawings of hypergraphs. In: Tollis and Patrignani (2009), pp. 396–407. 87, 88
Kaufmann, M., Wagner, D. (Eds.), 2001. Drawing Graphs: Methods and Models.
Vol. 2025 of Lecture Notes in Computer Science. Springer. 1
Kaufmann, M., Wagner, D. (Eds.), 2007. Proceedings of the 14th International Symposium on Graph Drawing (GD ’06). Vol. 4372 of Lecture Notes in Com-puter Science. Springer. 114, 117
Kaufmann, M., Wiese, R., 2002. Embedding vertices at points: Few bends suffice for planar graphs. Journal of Graph Algorithms and Applications 6 (1), 115–
129. 39
Korach, E., Stern, M., 2003. The clustering matroid and the optimal clustering tree. Mathematical Programming, Series B 98, 385 – 414. 87
Kosub, S., Maaß, M. G., T¨aubig, H., 2006. Acyclic type-of-relationship problems on the Internet. In: Erlebach, T. (Ed.), Proc. 3rd Workshop Combinatorial and Algorithmic Aspects of Networking (CAAN ’06). Vol. 4235 of Lecture Notes in Computer Science. Springer, pp. 98–111. 72
Kr´al’, D., Kratochv´ıl, J., Voss, H.-J., 2004. Mixed hypercacti. Discrete Mathe-matics 286, 99–113. 87
Lee, Y.-Y., Lin, C.-C., Yen, H.-C., 2006. Mental map preserving graph drawing using simulated annealing. In: Misue, K., Sugiyama, K., Tanaka, J. (Eds.), Proceedings of the 2006 Asia-Pacific Symposium on Information Visualisation (APVis ’06). Australian Computer Society, pp. 179–188. 55
Lipton, R. J., Rose, D. J., Tarjan, R. E., 1979. Generalized nested dissection.
SIAM Journal on Numerical Analysis 16 (2), 346–358. 34
Melan¸con, G., Herman, I., 1998. Circular drawing of rooted trees. Technical report 9817, Reports of the Centre for Mathematics and Computer Science.
URL http://www.cwi.nl/InfoVis/papers/circular.pdf 12
Merrick, D., Gudmundsson, J., 2007. Path simplification for metro map layout.
In: Kaufmann and Wagner (2007), pp. 258–269. 55
Michener, C. D., Sokal, R. R., 1957. A quantitative approach to a problem in classification. Evolution 11 (2), 130–162. 19
Misue, K., Eades, P., Lai, W., Sugiyama, K., 1995. Layout adjustment and the mental map. Journal on Visual Languages and Computing 6 (2), 183–210. IV, 55
Neyer, G., 1999. Line simplification with restricted orientations. In: Dehne, F., Gupta, A., Sack, J.-R., Tamassia, R. (Eds.), Proceedings of the 6th Workshop on Algorithms and Data Structures (WADS ’99). Vol. 1663 of Lecture Notes in Computer Science. Springer, pp. 13–24. 55
N¨ollenburg, M., 2010. An improved algorithm for the metro-line crossing mini-mization problem. In: Eppstein and Gansner (2010), pp. 381–392. 89
N¨ollenburg, M., Wolff, A., 2006. A mixed-integer program for drawing high-quality metro maps. In: Healy and Nikolov (2006), pp. 321–333. 55
Opatrny, J., 1979. Total ordering problems. SIAM Journal on Computing 8 (1), 111–114. 71, 72, 92, 93
Pach, J., Wenger, R., 1998. Embedding planar graphs at fixed vertex locations.
In: Whitesides (1998), pp. 263–274. 39
Page, R. D. M., 2000. TreeView. http://taxonomy.zoology.gla.ac.uk/rod/
treeview.html, university of Glasgow. 16
PHYLIP, 1993. PHYLIP. Phylogeny inference package.
http://evolution.genetics.washington.edu/phylip.html. 16, 22
Purchase, H. C., 1997. Which aesthetic has the greatest effect on human un-derstanding? In: Di Battista, G. (Ed.), Proceedings of the 5th International Symposium on Graph Drawing (GD ’97). Vol. 1353 of Lecture Notes in Com-puter Science. Springer, pp. 248–261. 1
Reingold, E. M., Tilford, J. S., 1981. Tidier drawing of trees. IEEE Transactions on Software Engineering 7 (2), 223–228. 12
Saitou, N., Nei, M., 1987. The neighbor-joining method: A new method for reconstructing phylogenetic trees. Molecular Biology and Evolution 4 (4), 406–
425. 19
Simonetto, P., Auber, D., Archambault, D., 2009. Fully automatic visualisation of overlapping sets. Computer Graphics Forum 28 (3), 967–974. 87
Sugiyama, K., 2002. Graph Drawing and Applications for Software and Knowl-edge Engineers. World Scientific. 1
Swofford, D. L., 2002. PAUP∗. Phylogenetic analysis using parsimony (and other methods). http://paup.csit.fsu.edu/, florida State University. 16
Swofford, D. L., Olsen, G. J., Waddell, J., Hillis, D. M., 1996. Phylogenetic infer-ence. In: Hillis, D. M., Moritz, C., Mable, B. (Eds.), Molecular Systematics, 2nd Edition. Sinauer Associates, pp. 407–514. 16
Tarjan, R. E., Yannakakis, M., 1984. Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal on Computing 13 (3), 566–579. 87, 106 Tischler, G., Radzik, T. (Eds.), 2010. Proceedings of the 21st International
Work-shop on Combinatorial Algorithms (IWOCA 2010). Vol. 6460 of Lecture Notes in Computer Science. Springer. 113
Tollis, I. G., Patrignani, M. (Eds.), 2009. Proceedings of the 16th International Symposium on Graph Drawing (GD 2008). Vol. 5417 of Lecture Notes in Computer Science. Springer. 113, 117
Tutte, W. T., 1960. Convex representations of graphs. Proceedings of the London Mathematical Society, Third Series 10, 304–320. 30
Tutte, W. T., 1963. How to draw a graph. Proceedings of the London Mathe-matical Society, Third Series 13, 743–767. 30
Walker, J. Q., 1990. A node-positioning algorithm for general trees. Software—
Practice and Experience 20 (7), 685–705. 12
Whitesides, S. H. (Ed.), 1998. Proceedings of the 6th International Symposium on Graph Drawing (GD ’98). Vol. 1547 of Lecture Notes in Computer Science.
Springer. 114, 118
Wiese, R., Eiglsperger, M., Kaufmann, M., 2002. yFiles: Visualization and au-tomatic layout of graphs. In: Mutzel, P., J¨unger, M., Leipert, S. (Eds.), Pro-ceedings of the 9th International Symposium on Graph Drawing (GD ’01).
Vol. 2265 of Lecture Notes in Computer Science. Springer, pp. 453–454. 16, 37
Wolff, A., 1970. Drawing subway maps: A survey. Informatik-Forschung und Entwicklung 22, 23–44. 89
Yannakakis, M., 1982. The complexity of the partial order dimension problem.
SIAM Journal on Algebraic and Discrete Methods 3 (3), 351–358. 72
Index
MONOTONE 3-SAT, 10, 56, 57 acyclicity, 71
adjacent, 2, 7, 11
algorithm, 19, 22, 23, 38, 55, 89 linear time, 12, 16
resolution, 3, 12, 23, 39 width, 21, 26 constraint, 1, 11, 38, 55, 67, 93
angle constraint, 2, 11, 38, 50
distance constraint, 2, 11, 16, 38,
counterclockwise, 9, 11, 12, 22, 24, 41 crossing
straight-line, 3, 22, 38, 39, 71, 90 tree drawing, 16
edge, 1, 7, 12, 38 crossing, 39 curved, 39 directed, 7
framing edge, 57, 63, 67 length, 4, 11, 16, 55, 56 literal edge, 57, 63, 67 multiple, 7
undirected, 7
embedding-constrained, 55 equation, 34
error, 36
Euler diagram, 5, 8, 87, 94 Euler tour, 38
embedded, 9, 11 hypergraph, 5, 8, 72, 87
coloring, 87 intersection, 12, 39, 42, 45, 90 invariant characteristic, 38
linear time, 23, 38, 50, 106
link, 57
orthogonal, 3, 9, 55, 56 total, 9
parent, 7, 12, 38
path, 5, 7, 23, 38, 56, 71, 72 clause path, 72
Hamiltonian path, 71, 88, 94 length, 7
planarity, 19, 32, 34, 40 plane, 39, 56, 89
point, 39
splitting point, 50 polygonal chain, 21, 38 polyline, 12, 38, 40, 46
planar, 38 draw-ing problem, 71, 83, 92
trajectory drawing problem, 4, 71
property, 35
rotation, 18, 21, 38, 44 run time, 35, 105
realizability, 11, 38 monotone path-based, 89, 92, 93 outerplanar, 88
phylogenetic tree, 2, 16, 18 rooted, 18