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L-Drawings of Directed Graphs

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9587)

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.

Keywords

  • Directed Graph
  • Vertical Segment
  • Random Placement
  • Horizontal Segment
  • Directed Cycle

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

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Notes

  1. 1.

    Refer to [6]. A formal proof of the equivalence of the two problems can be found in [12].

References

  1. 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)

    Google Scholar 

  2. 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)

    Google Scholar 

  3. Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Englewood Cliffs (1999)

    MATH  Google Scholar 

  4. 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)

    CrossRef  Google Scholar 

  5. 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)

    MATH  CrossRef  Google Scholar 

  6. Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Surv. 34(3), 313–356 (2002)

    CrossRef  Google Scholar 

  7. 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)

    MATH  MathSciNet  CrossRef  Google Scholar 

  8. Didimo, W., Montecchiani, F., Pallas, E., Tollis, I.G.: How to visualize directed graphs: a user study. In: IISA 2014, pp. 152–157. IEEE

    Google Scholar 

  9. Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)

    MATH  MathSciNet  CrossRef  Google Scholar 

  10. 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)

    CrossRef  Google Scholar 

  11. Golovach, P.: The total vertex separation number of a graph. Disk. Mat. 9(4), 86–91 (1997)

    MathSciNet  CrossRef  Google Scholar 

  12. Golovach, P., Fomin, F.: The total vertex separation number and the profile of graphs. Disk. Mat. 10(1), 87–94 (1998)

    MathSciNet  CrossRef  Google Scholar 

  13. Grinberg, E., Dambit, J.: Latviiskii Matematicheskii Ezhegodnik 2, 65–70 (1966). in Russian

    MATH  MathSciNet  Google Scholar 

  14. Gurobi Optimization: Gurobi Optimizer. http://www.gurobi.com/

  15. Healy, P., Nikolov, N.S.: Hierarchical drawing algorithms. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization. CRC Press, Boca Raton (2013)

    Google Scholar 

  16. Henry, N., Fekete, J., McGuffin, M.J.: Nodetrix: a hybrid visualization of social networks. IEEE Trans. Vis. Comput. Graph. 13(6), 1302–1309 (2007)

    CrossRef  Google Scholar 

  17. Huang, J., Kang, Z.: A genetic algorithm for the feedback set problems. In: ICPACE 2003 (2003)

    Google Scholar 

  18. Huang, W., Hong, S., Eades, P.: Effects of crossing angles. In: PacificVis 2008. IEEE (2008)

    Google Scholar 

  19. Kornaropoulos, E.M., Tollis, I.G.: Overloaded orthogonal drawings. In: Speckmann, B. (ed.) GD 2011. LNCS, vol. 7034, pp. 242–253. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  20. 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)

    CrossRef  Google Scholar 

  21. 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)

    MATH  MathSciNet  Google Scholar 

  22. Los Alamos Nat. Lab.: NetworkX. http://networkx.lanl.gov/index.html

  23. Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE Trans. Syst. Man Cybern. 11(2), 109–125 (1981)

    MathSciNet  CrossRef  Google Scholar 

  24. yWorks: yEd Graph Editor. http://www.yworks.com/en/products/yfiles/yed/

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Correspondence to Giordano Da Lozzo .

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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

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  • DOI: https://doi.org/10.1007/978-3-662-49192-8_11

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