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L-Drawings of Directed Graphs

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SOFSEM 2016: Theory and Practice of Computer Science (SOFSEM 2016)

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.

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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)

    Chapter  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)

    Article  MATH  Google Scholar 

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

    Article  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)

    Article  MATH  MathSciNet  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)

    Article  MATH  MathSciNet  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)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  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)

    Article  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)

    Chapter  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)

    Chapter  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)

    Article  MathSciNet  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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