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Large Angle Crossing Drawings of Planar Graphs in Subquadratic Area

  • Patrizio Angelini
  • Giuseppe Di Battista
  • Walter Didimo
  • Fabrizio Frati
  • Seok-Hee Hong
  • Michael Kaufmann
  • Giuseppe Liotta
  • Anna Lubiw
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

Abstract

This paper describes algorithms for computing non-planar drawings of planar graphs in subquadratic area such that: (i) edge crossings are allowed only if they create large angles; (ii) the maximum number of bends per edge is bounded by a (small) constant.

Keywords

Planar Graph Curve Complexity Outerplanar Graph Graph Drawing Sublinear Function 
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.

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References

  1. 1.
    Ackerman, E., Fulek, R., Tóth, C.D.: Graphs that admit polyline drawings with few crossing angles. SIAM Journal on Discrete Mathematics 26(1), 305–320 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Angelini, P., Cittadini, L., Di Battista, G., Didimo, W., Frati, F., Kaufmann, M., Symvonis, A.: On the perspectives opened by right angle crossing drawings. Journal of Graph Algorithms and Applications 15(1), 53–78 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Argyriou, E.N., Bekos, M.A., Symvonis, A.: The Straight-Line RAC Drawing Problem Is NP-Hard. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 74–85. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Arikushi, K., Fulek, R., Keszegh, B., Moric, F., Tóth, C.D.: Graphs that admit right angle crossing drawings. Computational Geometry: Theory & Applications 45(4), 169–177 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bonichon, N., Le Saëc, B., Mosbah, M.: Optimal Area Algorithm for Planar Polyline Drawings. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 35–46. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Upper Saddle River (1999)zbMATHGoogle Scholar
  8. 8.
    Di Giacomo, E., Didimo, W., Liotta, G., Meijer, H.: Area, curve complexity, and crossing resolution of non-planar graph drawings. Theory of Computing Systems 49(3), 565–575 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Didimo, W., Eades, P., Liotta, G.: Drawing Graphs with Right Angle Crossings. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 206–217. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Didimo, W., Eades, P., Liotta, G.: Drawing graphs with right angle crossings. Theoretical Computer Science 412(39), 5156–5166 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Diestel, R.: Graph Theory. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  12. 12.
    Diks, K., Djidjev, H., Sýkora, O., Vrto, I.: Edge separators of planar and outerplanar graphs with applications. J. Algorithms 14(2), 258–279 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Dujmović, V., Gudmundsson, J., Morin, P., Wolle, T.: Notes on large angle crossing graphs. Chicago Journal of Theoretical Computer Science, article 4, 1–14 (2011)Google Scholar
  14. 14.
    Frati, F., Patrignani, M.: A Note on Minimum-Area Straight-Line Drawings of Planar Graphs. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 339–344. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Huang, W.: Using eye tracking to investigate graph layout effects. In: Hong, S.H., Ma, K.L. (eds.) Asia-Pacific Symposium on Visualization (APVIS 2007), pp. 97–100. IEEE (2007)Google Scholar
  16. 16.
    Huang, W., Hong, S.H., Eades, P.: Effects of crossing angles. In: Pacific Visualization (PacificVis 2008), pp. 41–46. IEEE (2008)Google Scholar
  17. 17.
    Kaufmann, M., Wagner, D. (eds.): Drawing Graphs. LNCS, vol. 2025. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  18. 18.
    Korach, E., Solel, N.: Tree-width, path-widt, and cutwidth. Discrete Applied Mathematics 43(1), 97–101 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Schnyder, W.: Embedding planar graphs on the grid. In: Symposium on Discrete Algorithms (SODA 1990), pp. 138–148 (1990)Google Scholar
  20. 20.
    Tamassia, R., Tollis, I.G.: A unified approach to visibility representation of planar graphs. Discrete & Computational Geometry 1, 321–341 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Tamassia, R., Tollis, I.G.: Planar bookgrid embedding in linear time. IEEE Transactions on Cyrcuits and Systems 36(9), 1230–1234 (1989)CrossRefGoogle Scholar
  22. 22.
    Valiant, L.G.: Universality considerations in VLSI circuits. IEEE Transactions on Computers 30(2), 135–140 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Wood, D.R.: Grid drawings of k-colourable graphs. Computational Geometry: Theory & Applications 30(1), 25–28 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Giuseppe Di Battista
    • 1
  • Walter Didimo
    • 2
  • Fabrizio Frati
    • 3
  • Seok-Hee Hong
    • 3
  • Michael Kaufmann
    • 4
  • Giuseppe Liotta
    • 2
  • Anna Lubiw
    • 5
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreItaly
  2. 2.Dip. di Ingegneria Elettronica e dell’InformazionePerugia UniversityItaly
  3. 3.School of Information TechnologiesUniversity of SydneyAustralia
  4. 4.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  5. 5.Cheriton School of Computer ScienceUniversity of WaterlooCanada

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