Graph Compact Orthogonal Layout Algorithm

  • Kārlis FreivaldsEmail author
  • Jans Glagoļevs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8596)


There exist many orthogonal graph drawing algorithms that minimize edge crossings or edge bends, however they produce unsatisfactory drawings in many practical cases. In this paper we present a grid-based algorithm for drawing orthogonal graphs with nodes of prescribed size. It distinguishes by creating pleasant and compact drawings in relatively small running time. The main idea is to minimize the total edge length that implicitly minimizes crossings and makes the drawing easy to comprehend. The algorithm is based on combining local and global improvements. Local improvements are moving each node to a new place and swapping of nodes. Global improvement is based on constrained quadratic programming approach that minimizes the total edge length while keeping node relative positions.


Grid Cell Random Graph Manhattan Distance Visibility Graph Node Placement 
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.


  1. 1.
    Biedl, T., Kant, G.: A better heuristic for orthogonal graph drawings. Comput. Geom. 9(3), 159–180 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 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) CrossRefGoogle Scholar
  3. 3.
    Biedl, T.C., Madden, B.P., Tollis, I.G.: The three-phase method: a unified approach to orthogonal graph drawing. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 391–402. Springer, Heidelberg (1997) CrossRefGoogle Scholar
  4. 4.
    Bridgeman, S., Fanto, J., Garg, A., Tamassia, R., Vismara, L.: Interactivegiotto: an algorithm for interactive orthogonal graph drawing. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 303–308. Springer, Heidelberg (1997) CrossRefGoogle Scholar
  5. 5.
    Di Battista, G., Didimo, W., Patrignani, M., Pizzonia, M.: Orthogonal and Quasi-upward drawings with vertices of prescribed size. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 297–310. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  6. 6.
    Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Tassinari, E., Vargiu, F.: An experimental comparison of four graph drawing algorithms. Comput. Geom. 7(5), 303–325 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Dwyer, T., Marriott, K., Stuckey, P.J.: Fast node overlap removal. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 153–164. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  8. 8.
    Fößmeier, U., Heß, C., Kaufmann, M.: On improving orthogonal drawings: the 4M-Algorithm. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 125–137. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  9. 9.
    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) CrossRefGoogle Scholar
  10. 10.
    Freivalds, K., Kikusts, P.: Optimum layout adjustment supporting ordering constraints in graph-like diagram drawing. In: Proceedings of Latvian Academy of Sciences, Section B, No. 1, pp. 43–51 (2001)Google Scholar
  11. 11.
    Hachul, S., Jünger, M.: An experimental comparison of fast algorithms for drawing general large graphs. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 235–250. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  12. 12.
    Kojima, K., Nagasaki, M., Miyano, S.: Fast grid layout algorithm for biological networks with sweep calculation. Bioinformatics 24(12), 1433–1441 (2008)CrossRefGoogle Scholar
  13. 13.
    Kojima, K., Nagasaki, M., Miyano, S.: An efficient biological pathway layout algorithm combining grid-layout and spring embedder for complicated cellular location information. BMC Bioinformatics 11, 335 (2010)CrossRefGoogle Scholar
  14. 14.
    Lengauer, T.: Combinatorial algorithms for integrated circuit layout. John Wiley and Sons Inc., New York (1990)zbMATHGoogle Scholar
  15. 15.
    Li, W., Kurata, H.: A grid layout algorithm for automatic drawing of biochemical networks. Bioinformatics 21(9), 2036–2042 (2005)CrossRefGoogle Scholar
  16. 16.
    Six, J.M., Kakoulis, K.G., Tollis, I.G., et al.: Techniques for the refinement of orthogonal graph drawings. J. Graph Algorithms Appl. 4(3), 75–103 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput. 16(3), 421–444 (1987)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia

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