Generalizing Geometric Graphs
Network visualization is essential for understanding the data obtained from huge real-world networks such as flight-networks, the AS-network or social networks. Although we can compute layouts for these networks reasonably fast, even the most recent display media are not capable of displaying these layouts in an adequate way. Moreover, the human viewer may be overwhelmed by the displayed level of detail. The increasing amount of data therefore requires techniques aiming at a sensible reduction of the visual complexity of huge layouts.
We consider the problem of computing a generalization of a given layout reducing the complexity of the drawing to an amount that can be displayed without clutter and handled by a human viewer. We take a first step at formulating graph generalization within a mathematical model and we consider the resulting problems from an algorithmic point of view. Although these problems are NP-hard in general, we provide efficient approximation algorithms as well as efficient and effective heuristics. At the end of the paper we showcase some sample generalizations.
KeywordsEdge Incident Large Graph Geometric Graph Local Coverage Human Viewer
- 2.Abello, J., Korn, J., Finocchi, I.: Graph sketches. In: Proceedings of the IEEE Symposium on Information Visualization 2001 (INFOVIS 2001), p. 67. IEEE Computer Society (2001)Google Scholar
- 4.Bohn, R.E., Short, J.E.: How much information? 2009 Report on American consumers. Global Information Industry Center, University of California, San Diego (2009)Google Scholar
- 6.Brunel, E., Gemsa, A., Krug, M., Rutter, I., Wagner, D.: Generalizing Geometric Graphs. Technical Report 27, Karlsruhe Institute of Technology (2011)Google Scholar
- 10.Davis, T.A.: University of florida sparse matrix collection. NA Digest 92 (1994)Google Scholar
- 17.Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman and Company (1979)Google Scholar
- 22.Holten, D., van Wijk, J.J.: Force-directed edge bundling for graph visualization. In: Proc. of the 11th Eurographics/IEEE-VGTC Symp. on Vis, pp. 983–990 (2009)Google Scholar
- 25.Mackaness, W.A., Ruas, A., Sarjakoski, L.T. (eds.): Generalisation of Geographic Information. Cartographic Modelling and Applications. Elsevier B.V. (2007)Google Scholar
- 27.Openstreetmap database (2011), http://www.openstreetmap.de/
- 30.Sarkar, M., Brown, M.H.: Graphical fisheye views of graphs. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI 1992, pp. 83–91. ACM, New York (1992)Google Scholar