Abstract
We introduce L-drawings, a novel paradigm for representing directed graphs aiming at combining the readability features of orthogonal drawings with the expressive power of matrix representations. In an L-drawing, vertices have exclusive x- and y-coordinates and edges consist of two segments, one exiting the source vertically and one entering the destination horizontally.
We study the problem of computing L-drawings using minimum ink. We prove its NP-completeness and provide a heuristic based on a polynomial-time algorithm that adds a vertex to a drawing using the minimum additional ink. We performed an experimental analysis of the heuristic which confirms its effectiveness.
Angelini was partially supported by DFG grant Ka812/17-1. Da Lozzo, Di Bartolomeo, Di Donato, Patrignani, and Roselli were partially supported by MIUR project “AMANDA – Algorithmics for MAssive and Networked DAta”, prot. 2012C4E3KT_001.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Angelini, P., Da Lozzo, G., Di Bartolomeo, M., Di Donato, V., Patrignani, M., Roselli, V., Tollis, I.G.: L-drawings of directed graphs. CoRR abs/1509.00684 (2015)
Biedl, T.C., Kaufmann, M.: Area-efficient static and incremental graph drawings. In: Burkard, R., Woeginger, G. (eds.) ESA 1997. LNCS, vol. 1284, pp. 37–52. Springer, Heidelberg (1997)
Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Englewood Cliffs (1999)
Díaz, J., Gibbons, A., Paterson, M., Toran, J.: The MINSUMCUT problem. In: Dehne, F., Sack, J., Santoro, N. (eds.) WADS 1991. LNCS, vol. 519, pp. 65–79. Springer, Heidelberg (1991)
Díaz, J., Penrose, M., Petit, J., Serna, M.: Convergence theorems for some layout measures on random lattice and random geometric graphs. Comb. Prob. Comput. 9(6), 489–511 (2000)
Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Surv. 34(3), 313–356 (2002)
Dickerson, M., Eppstein, D., Goodrich, M.T., Meng, J.Y.: Confluent drawings: visualizing non-planar diagrams in a planar way. J. Graph Alg. Appl. 9(1), 31–52 (2005)
Didimo, W., Montecchiani, F., Pallas, E., Tollis, I.G.: How to visualize directed graphs: a user study. In: IISA 2014, pp. 152–157. IEEE
Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)
Ghoniem, M., Fekete, J., Castagliola, P.: On the readability of graphs using node-link and matrix-based representations: a controlled experiment and statistical analysis. Inf. Vis. 4(2), 114–135 (2005)
Golovach, P.: The total vertex separation number of a graph. Disk. Mat. 9(4), 86–91 (1997)
Golovach, P., Fomin, F.: The total vertex separation number and the profile of graphs. Disk. Mat. 10(1), 87–94 (1998)
Grinberg, E., Dambit, J.: Latviiskii Matematicheskii Ezhegodnik 2, 65–70 (1966). in Russian
Gurobi Optimization: Gurobi Optimizer. http://www.gurobi.com/
Healy, P., Nikolov, N.S.: Hierarchical drawing algorithms. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization. CRC Press, Boca Raton (2013)
Henry, N., Fekete, J., McGuffin, M.J.: Nodetrix: a hybrid visualization of social networks. IEEE Trans. Vis. Comput. Graph. 13(6), 1302–1309 (2007)
Huang, J., Kang, Z.: A genetic algorithm for the feedback set problems. In: ICPACE 2003 (2003)
Huang, W., Hong, S., Eades, P.: Effects of crossing angles. In: PacificVis 2008. IEEE (2008)
Kornaropoulos, E.M., Tollis, I.G.: Overloaded orthogonal drawings. In: Speckmann, B. (ed.) GD 2011. LNCS, vol. 7034, pp. 242–253. Springer, Heidelberg (2011)
Kornaropoulos, E.M., Tollis, I.G.: DAGView: An Approach for Visualizing Large Graphs. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 499–510. Springer, Heidelberg (2013)
Lin, Y., Yuan, J.: Profile minimization problem for matrices and graphs. Acta Mathematicae Applicatae Sinica. English Series. Yingyong. Shuxue Xuebao 10(1), 107–112 (1994)
Los Alamos Nat. Lab.: NetworkX. http://networkx.lanl.gov/index.html
Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE Trans. Syst. Man Cybern. 11(2), 109–125 (1981)
yWorks: yEd Graph Editor. http://www.yworks.com/en/products/yfiles/yed/
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Angelini, P. et al. (2016). L-Drawings of Directed Graphs. In: Freivalds, R., Engels, G., Catania, B. (eds) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016. Lecture Notes in Computer Science(), vol 9587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49192-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-662-49192-8_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-49191-1
Online ISBN: 978-3-662-49192-8
eBook Packages: Computer ScienceComputer Science (R0)