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Extending Partial Orthogonal Drawings

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Graph Drawing and Network Visualization (GD 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12590))

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Abstract

We study the planar orthogonal drawing style within the framework of partial representation extension. Let \((G,H,\varGamma _H)\) be a partial orthogonal drawing, i.e., G is a graph, \(H\subseteq G\) is a subgraph and \(\varGamma _H\) is a planar orthogonal drawing of H.

We show that the existence of an orthogonal drawing \(\varGamma _G\) of G that extends \(\varGamma _H\) can be tested in linear time. If such a drawing exists, then there also is one that uses O(|V(H)|) bends per edge. On the other hand, we show that it is NP-complete to find an extension that minimizes the number of bends or has a fixed number of bends per edge.

The full version of this article is available at ArXiv [3].

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References

  1. Angelini, P., et al.: Simultaneous orthogonal planarity. In: Hu, Y., Nöllenburg, M. (eds.) GD 2016. LNCS, vol. 9801, pp. 532–545. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-50106-2_41

    Chapter  Google Scholar 

  2. Angelini, P., et al.: Testing planarity of partially embedded graphs. ACM Trans. Algorithm. 11(4), 32:1–32:42 (2015). https://doi.org/10.1145/2629341

    Article  MathSciNet  MATH  Google Scholar 

  3. Angelini, P., Rutter, I., T.P., S.: Extending partial orthogonal drawings (2020). https://arxiv.org/abs/2008.10280

  4. Bläsius, T., Lehmann, S., Rutter, I.: Orthogonal graph drawing with inflexible edges. Comput. Geom. 55, 26–40 (2016). https://doi.org/10.1016/j.comgeo.2016.03.001

    Article  MathSciNet  MATH  Google Scholar 

  5. Bläsius, T., Rutter, I., Wagner, D.: Optimal orthogonal graph drawing with convex bend costs. ACM Trans. Algorithm. 12(3), 33:1–33:32 (2016). https://doi.org/10.1145/2838736

    Article  MathSciNet  MATH  Google Scholar 

  6. Chan, T.M., Frati, F., Gutwenger, C., Lubiw, A., Mutzel, P., Schaefer, M.: Drawing partially embedded and simultaneously planar graphs. J. Graph Algorithm. Appl. 19(2), 681–706 (2015). https://doi.org/10.7155/jgaa.00375

    Article  MathSciNet  MATH  Google Scholar 

  7. Chaplick, S., Dorbec, P., Kratochvíl, J., Montassier, M., Stacho, J.: Contact representations of planar graphs: extending a partial representation is hard. In: Kratsch, D., Todinca, I. (eds.) WG 2014. LNCS, vol. 8747, pp. 139–151. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12340-0_12

    Chapter  Google Scholar 

  8. Chaplick, S., Fulek, R., Klavík, P.: Extending partial representations of circle graphs. J. Graph Theory 91(4), 365–394 (2019). https://doi.org/10.1002/jgt.22436

    Article  MathSciNet  MATH  Google Scholar 

  9. de Berg, M., Khosravi, A.: Optimal binary space partitions for segments in the place. Int. J. Comput. Geom. Appl. 22(3), 187–205 (2012)

    Article  Google Scholar 

  10. Di Battista, G., Liotta, G., Vargiu, F.: Spirality and optimal orthogonal drawings. SIAM J. Comput. 27(6), 1764–1811 (1998). https://doi.org/10.1137/S0097539794262847

    Article  MathSciNet  MATH  Google Scholar 

  11. Didimo, W., Liotta, G.: Computing orthogonal drawings in a variable embedding setting. In: Chwa, K.-Y., Ibarra, O.H. (eds.) ISAAC 1998. LNCS, vol. 1533, pp. 80–89. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-49381-6_10

    Chapter  Google Scholar 

  12. Didimo, W., Liotta, G., Ortali, G., Patrignani, M.: Optimal orthogonal drawings of planar 3-graphs in linear time. In: Chawla, S. (ed.) Proceedings of the 30th ACM-SIAM Symposium on Discrete Algorithms (SODA’20), pp. 806–825. SIAM (2020). https://doi.org/10.1137/1.9781611975994.49

  13. Duncan, C.A., Goodrich, M.T.: Planar orthogonal and polyline drawing algorithms. In: Tamassia, R. (ed.) Handbook on Graph Drawing and Visualization, pp. 223–246. Chapman and Hall/CRC (2013)

    Google Scholar 

  14. Eiben, E., Ganian, R., Hamm, T., Klute, F., Nöllenburg, M.: Extending partial 1-planar drawings. In: Czumaj, A., Dawar, A., Merelli, E. (eds.) 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), vol. 168, pp. 43:1–43:19. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany (2020). https://doi.org/10.4230/LIPIcs.ICALP.2020.43, https://drops.dagstuhl.de/opus/volltexte/2020/12450

  15. Eppstein, D.: Graph-theoretic solutions to computational geometry problems. In: Paul, C., Habib, M. (eds.) WG 2009. LNCS, vol. 5911, pp. 1–16. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11409-0_1

    Chapter  Google Scholar 

  16. Fößmeier, U., Kaufmann, M.: Drawing high degree graphs with low bend numbers. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 254–266. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0021809

    Chapter  Google Scholar 

  17. Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001). https://doi.org/10.1137/S0097539794277123

    Article  MathSciNet  MATH  Google Scholar 

  18. Jelínek, V., Kratochvíl, J., Rutter, I.: A Kuratowski-type theorem for planarity of partially embedded graphs. Comput. Geom. 46(4), 466–492 (2013). https://doi.org/10.1016/j.comgeo.2012.07.005

    Article  MathSciNet  MATH  Google Scholar 

  19. Klavík, P., et al.: Extending partial representations of proper and unit interval graphs. Algorithmica 77(4), 1071–1104 (2016). https://doi.org/10.1007/s00453-016-0133-z

    Article  MathSciNet  MATH  Google Scholar 

  20. Klavík, P., Kratochvíl, J., Otachi, Y., Saitoh, T.: Extending partial representations of subclasses of chordal graphs. Theor. Comput. Sci. 576, 85–101 (2015). https://doi.org/10.1016/j.tcs.2015.02.007

    Article  MathSciNet  MATH  Google Scholar 

  21. Klavík, P., Kratochvíl, J., Otachi, Y., Saitoh, T., Vyskočil, T.: Extending partial representations of interval graphs. Algorithmica 78(3), 945–967 (2016). https://doi.org/10.1007/s00453-016-0186-z

    Article  MathSciNet  MATH  Google Scholar 

  22. Knuth, D.E., Raghunathan, A.: The problem of compatible representatives. SIAM J. Discret. Math. 5(3), 422–427 (1992). https://doi.org/10.1137/0405033

    Article  MathSciNet  MATH  Google Scholar 

  23. Krawczyk, T., Walczak, B.: Extending partial representations of trapezoid graphs. In: Bodlaender, H.L., Woeginger, G.J. (eds.) WG 2017. LNCS, vol. 10520, pp. 358–371. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68705-6_27

    Chapter  Google Scholar 

  24. Pach, J., Wenger, R.: Embedding planar graphs at fixed vertex locations. Graphs Comb. 17, 717–728 (2001)

    Article  MathSciNet  Google Scholar 

  25. Patrignani, M.: On extending a partial straight-line drawing. Int. J. Found. Comput. Sci. 17(5), 1061–1070 (2006). https://doi.org/10.1142/S0129054106004261

    Article  MathSciNet  MATH  Google Scholar 

  26. Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. J. Comput. 16(3), 421–444 (1987)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. John Cabot University, Rome, Italy

    Patrizio Angelini

  2. Universität Passau, 94032, Passau, Germany

    Ignaz Rutter & T. P. Sandhya

Authors
  1. Patrizio Angelini
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  2. Ignaz Rutter
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  3. T. P. Sandhya
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Corresponding author

Correspondence to T. P. Sandhya .

Editor information

Editors and Affiliations

  1. LaBRI, University of Bordeaux, Talence, France

    David Auber

  2. Charles University, Prague, Czech Republic

    Pavel Valtr

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Angelini, P., Rutter, I., Sandhya, T.P. (2020). Extending Partial Orthogonal Drawings. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_21

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  • DOI: https://doi.org/10.1007/978-3-030-68766-3_21

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  • Online ISBN: 978-3-030-68766-3

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