Progress on Partial Edge Drawings

Bruckdorfer, Till and Cornelsen, Sabine and Gutwenger, Carsten and Kaufmann , Michael and Montecchiani, Fabrizio and Nöllenburg, Martin and Wolff, Alexander (2013) Progress on Partial Edge Drawings. In: 20th International Symposium, GD 2012, September 19-21, 2012, Redmond, WA, USA , pp. 67-78 (Official URL: http://link.springer.com/chapter/10.1007/978-3-642-36763-2_7).

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Abstract

Recently, a new way of avoiding crossings in straight-line drawings of non-planar graphs has been investigated. The idea of partial edge drawings (PED) is to drop the middle part of edges and rely on the remaining edge parts called stubs. We focus on a symmetric model (SPED) that requires the two stubs of an edge to be of equal length. In this way, the stub at the other endpoint of an edge assures the viewer of the edge's existence. We also consider an additional homogeneity constraint that forces the stub lengths to be a given fraction δ of the edge lengths (δ-SHPED). Given length and direction of a stub, this model helps to infer the position of the opposite stub. We show that, for a fixed stub---edge length ratio δ, not all graphs have a δ-SHPED. Specifically, we show that $K_241$ does not have a 1/4-SHPED, while bandwidth-k graphs always have a $\Theta(1/\sqrt{k})$-SHPED. We also give bounds for complete bipartite graphs. Further, we consider the problem MaxSPED where the task is to compute the SPED of maximum total stub length that a given straight-line drawing contains. We present an efficient solution for 2-planar drawings and a 2-approximation algorithm for the dual problem.

Item Type:Conference Paper
Additional Information:10.1007/978-3-642-36763-2_7
Classifications:P Styles > P.720 Straight-line
P Styles > P.999 Others
ID Code:1298

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References

Bar-Yehuda, R., Rawitz, D.: Efficient algorithms for integer programs with two variables per constraint. Algorithmica 29, 595–609 (2001)

Becker, R.A., Eick, S.G., Wilks, A.R.: Visualizing network data. IEEE Trans. Visual. Comput. Graphics 1(1), 16–28 (1995)

Bentley, J.L., Ottmann, T.A.: Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput. 28(9), 643–647 (1979)

Bruckdorfer, T., Cornelsen, S., Gutwenger, C., Kaufmann, M., Montecchiani, F., Nöllenburg, M., Wolff, A.: Progress on partial edge drawings. Arxiv, arxiv.org/abs/1209.0830 (2012)

Bruckdorfer, T., Kaufmann, M.: Mad at Edge Crossings? Break the Edges! In: Kranakis, E., Krizanc, D., Luccio, F. (eds.) FUN 2012. LNCS, vol. 7288, pp. 40–50. Springer, Heidelberg (2012)

Burch, M., Vehlow, C., Konevtsova, N., Weiskopf, D.: Evaluating Partially Drawn Links for Directed Graph Edges. In: van Kreveld, M., Speckmann, B. (eds.) GD 2011. LNCS,

vol. 7034, pp. 226–237. Springer, Heidelberg (2012)

Dickerson, M., Eppstein, D., Goodrich, M.T., Meng, J.Y.: Confluent drawings: Visualizing non-planar diagrams in a planar way. J. Graph Algorithms Appl. 9(1), 31–52 (2005)

Eppstein, D., van Kreveld, M., Mumford, E., Speckmann, B.: Edges and switches, tunnels and bridges. Comput. Geom. Theory Appl. 42(8), 790–802 (2009)

Erdős, P., Szekeres, G.: A combinatorial problem in geometry. Compositio Mathematica 2, 463–470 (1935)

Gansner, E., Hu, Y., North, S., Scheidegger, C.: Multilevel agglomerative edge bundling for visualizing large graphs. In: 4th IEEE Pacific Visual. Symp. (PacificVis 2011), pp. 187–194. IEEE Press, New York (2011)

Håstad, J.: Clique is hard to approximate within n 1 − ε . Acta Math. 182, 105–142 (1999)

Holten, D., van Wijk, J.J.: Force-directed edge bundling for graph visualization. Comput. Graphics Forum 28(3), 983–990 (2009)

Kindermann, P., Spoerhase, J.: Private Communication (March 2012)

Pach, J., Tóth, G.: Graphs drawn with few crossings per edge. Combin. 17, 427–439 (1997)

Peng, D., Lu, N., Chen, W., Peng, Q.: SideKnot: Revealing relation patterns for graph visualization. In: 5th IEEE Pacific Visual. Symp. (PacificVis 2012), pp. 65–72.IEEE Press, New York (2012)

Porschen, S., Speckenmeyer, E.: Algorithms for Variable-Weighted 2-SAT and Dual Problems. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 173–186. Springer, Heidelberg (2007)

Rusu, A., Fabian, A.J., Jianu, R., Rusu, A.: Using the gestalt principle of closure to alleviate the edge crossing problem in graph drawings. In: 15th Int. Conf. Inform. Visual. (IV 2011), pp. 488–493. IEEE Press, New York (2011)