Refinement of Orthogonal Graph Drawings
Current orthogonal graph drawing algorithms produce drawings which are generally good. However, many times the readability of orthogonal drawings can be significantly improved with a postprocessing technique, called refinement, which improves aesthetic qualities of a drawing such as area, bends, crossings, and total edge length. Refinement is separate from layout and works by analyzing and then fine-tuning the existing drawing in an efficient manner. In this paper we define the problem and goals of orthogonal drawing refinement and introduce a methodology which efficiently refines any orthogonal graph drawing. We have implemented our technique in C++ and conducted preliminary experiments over a set of drawings from five well known orthogonal drawing systems. Experimental analysis shows our technique to produce an average 34% improvement in area, 22% in bends, 19% in crossings, and 34% in total edge length.
- 1.T. Biedl and G. Kant, A Better Heuristic for Orthogonal Graph Drawings, Proc. ESA’94, LNCS 855, Springer-Verlag, 1994, pp. 24–35.Google Scholar
- 2.T. C. Biedl, B. P. Madden and I. G. Tollis, The Three-Phase Method: A Unified Approach to Orthogonal Graph Drawing, Proc. GD’97, LNCS 1353, Springer-Verlag, 1997, pp. 391–402.Google Scholar
- 3.S. Bridgeman, J. Fanto, A. Garg, R. Tamassia and L. Vismara, Interactive Giotto: An Algorithm for Interactive Orthogonal Graph Drawing, Proc. GD’ 97, LNCS1353, Springer-Verlag, 1997, pp. 303–308.Google Scholar
- 4.S. Bridgeman, A. Garg and R. Tamassia, A Graph Drawing and Translation Service on the WWW, Proc. GD’ 96, LNCS 1190, Springer-Verlag, 1997, pp. 45–52.Google Scholar
- 5.R. F. Cohen, G. Di Battista, R. Tamassia and I. G. Tollis, Dynamic Graph Drawings: Trees, Series-Parallel Digraphs, and Planar ST-Digraphs, SIAM J. Computing, 24(5), October 1995, pp. 970–1001.Google Scholar
- 7.G. Di Battista, A. Garg, G. Liotta, R. Tamassia, E. Tassinari and F. Vargiu, An Experimental Comparison of Four Graph Drawing Algorithms, Computational Geometry: Theory and Applications, 1997, pp. 303–325.Google Scholar
- 11.S. Even and G. Granot, Rectilinear Planar Drawings with Few Bends in Each Edge, Tech. Report 797, CS Dept., Technion, Israel Inst. of Tech., 1994.Google Scholar
- 12.Jody Fanto, Postprocessing of GIOTTO drawings, http://www.cs.brown.edu/ people/jrf/.
- 13.U. Fößmeier, Interactive Orthogonal Graph Drawing: Algorithms and Bounds, Proc. GD’ 97, LNCS 1353, Springer-Verlag, 1997, pp. 111–123.Google Scholar
- 14.U. Fößmeier and M. Kaufmann, Algorithms and Area Bounds for Nonplanar Orthogonal Drawings, Proc. GD’ 97, LNCS 1353, Springer-Verlag, 1997, pp. 134–145.Google Scholar
- 15.M. Y. Hsueh, Symbolic Layout and Compaction of Integrated Circuits, Ph.D. Thesis, University of California at Berkeley, Berkeley,CA, 1979.Google Scholar
- 16.G. Kant, Drawing Planar Graphs Using the lmc-ordering, Proc. 33rd Ann. IEEE Symposium on Found. of Comp. Sci., 1992, pp. 101–110.Google Scholar
- 18.Thomas Lengauer, Combinatorial Algorithms for Integrated Circuit Layout, John Wiley and Sons, 1990.Google Scholar
- 19.K. Miriyala, S. W. Hornick and R. Tamassia, An Incremental Approach to Aesthetic Graph Layout, Proc. Int. Workshop on Computer-Aided Software Engineering (Case)’ 93 ), 1993, pp. 297–308.Google Scholar
- 20.K. Misue, P. Eades, W. Lai and K. Sugiyama, Layout Adjustment and the Mental Map, J. of Visual Languages and Computing, June 1995, pp. 183–210.Google Scholar
- 21.A. Papakostas, Information Visualization: Orthogonal Drawings of Graphs, Ph.D. Thesis, University of Texas at Dallas, 1996.Google Scholar
- 22.A. Papakostas, J. M. Six and I. G. Tollis, Experimental and Theoretical Results in Interactive Orthogonal Graph Drawing, Proc. GD’ 96, LNCS 1190, Springer-Verlag, 1997, pp. 371–386.Google Scholar
- 25.H. Purchase, Which Aesthetic has the Greatest Effect on Human Understanding, Proc. of GD’ 97, LNCS 1353, Springer-Verlag, 1997, pp. 248–261.Google Scholar
- 29.R. Tamassia and I. G. Tollis, Planar Grid Embeddings in Linear Time, IEEE Trans. on Circuits and Systems CAS-36, 1989, pp. 1230–1234.Google Scholar
- 30.I. G. Tollis, Graph Drawing and Information Visualization, ACM Computing Surveys, 28A(4), December 1996. Also available at http://www.utdallas.edu/ ~tollis/SDCR96/TollisGeometry/.