Graph Drawing by Stress Majorization
One of the most popular graph drawing methods is based on achieving graph-theoretic target distances. This method was used by Kamada and Kawai , who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In this work, we show how to draw graphs by stress majorization, adapting a technique known in the MDS community for more than two decades. It appears that majorization has advantages over the technique of Kamada and Kawai in running time and stability. We also found the majorization-based optimization being essential to a few extensions to the basic energy model. These extensions can improve layout quality and computation speed in practice.
- 8.Gajer, P., Goodrich, M.T., Kobourov, S.G.: A Multi-dimensional Approach to Force-Directed Layouts of Large Graphs. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 211–221. Springer, Heidelberg (2001)Google Scholar
- 9.Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press (1996)Google Scholar
- 14.Koren, Y.: Graph Drawing by Subspace Optimization. In: Proceedings 6th Joint Eurographics – IEEE TCVG Symposium Visualization (VisSym 2004). Eurographics, pp. 65–74 (2004)Google Scholar
- 17.Kruskal, J., Seery, J.: Designing network diagrams. In: Proceedings First General Conference on Social Graphics, pp. 22–50 (1980)Google Scholar
- 22.Intel Math Kernel Library, http://www.intel.com/software/products/mkl/
- 23.Automatically Tuned Linear Algebra Software (ATLAS), http://atlas.sourceforge.net/