Subscribe

Issue No.12 - Dec. (2012 vol.18)

pp: 2486-2495

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.238

ABSTRACT

We propose a technique that allows straight-line graph drawings to be rendered interactively with adjustable level of detail. The approach consists of a novel combination of edge cumulation with density-based node aggregation and is designed to exploit common graphics hardware for speed. It operates directly on graph data and does not require precomputed hierarchies or meshes. As proof of concept, we present an implementation that scales to graphs with millions of nodes and edges, and discuss several example applications.

INDEX TERMS

rendering (computer graphics), graph data, interactive level-of-detail rendering, straight-line graph drawings, edge cumulation, density-based node aggregation, common graphics hardware, Rendering (computer graphics), Aggregates, Image edge detection, Data visualization, Image color analysis, edge aggregation, Graph visualization, OpenGL

CITATION

M. Zinsmaier, U. Brandes, O. Deussen, H. Strobelt, "Interactive Level-of-Detail Rendering of Large Graphs",

*IEEE Transactions on Visualization & Computer Graphics*, vol.18, no. 12, pp. 2486-2495, Dec. 2012, doi:10.1109/TVCG.2012.238REFERENCES

- [1] Openstreetmap. http://openstreetmap.de, Jul 2011.
- [2] Sparse matrix collection. http://www.cise.ufl.edu/research/sparsematricesr. Jan 2012.
- [3] Us airtraffic dataset. http://www.transtats.bts.gov, Jan 2012.
- [4] J. Abello,F. van Ham,, and N. Krishnan., ASK-GraphView: A large scale graph visualization system.
IEEE Transactions on Visualization and Computer Graphics, 12(5): 669-676, 2006.- [5] R. A. Becker,S. G. Eick,, and A. R. Wilks., Visualizing network data
IEEE Transactions on Visualization and Computer Graphics, 1: 16-28, 1995.- [6] T. Buering, J. Gerken, and H. Reiterer, User interaction with scatterplots on small screens - a comparative evaluation of geometric-semantic zoom and fisheye distortion
IEEE Transactions on Visualization and Computer Graphics, 12(5): 829-836, Sept. 2006.- [7] N. Cao, J. Sun, Y. Lin., D. Gotz, S. Liu,, and H. Qu., Facetatlas: Multi-faceted visualization for rich text corpora.
Visualization and Computer Graphics, IEEE Transactions on, 16(6): 1172-1181, 2010.- [8] D. B. Carr,R. J. Littlefield,W. L. Nicholson,, and J. S. Littlefield., Scatterplot matrix techniques for large n
Journal of the American Statistical Association, 82(398): pp. 424-436, 1987.- [9] W. Cui, H. Zhou, H. Qu,P. C. Wong,, and X. Li., Geometry-based edge clustering for graph visualization.
IEEE Transactions on Visualization and Computer Graphics, 14(6): 1277-1284, Nov. 2008.- [10] M. Dickerson, D. Eppstein, M. Goodrich,, and J. Meng., Confluent drawings: Visualizing non-planar diagrams in a planar way. In G. Liotta,
editor, Graph Drawing, 2912 of Lecture Notes in Computer Sci-ence, pages 1-12. Springer Berlin / Heidelberg, 2004. 10.1007/978–3-540–24595-7 _1. - [11] O. Ersoy, C. Hurter, F. Paulovich., G. Cantareiro, and A. Telea, Skeleton-based edge bundling for graph visualization
IEEE Transactions on Visualization and Computer Graphics, 17(12): 2364-2373, Dec. 2011.- [12] E. R. Gansner, Y. Hu, S. North,, and C. Scheidegger., Multilevel agglom-erative edge bundling for visualizing large graphs. In
Proceedings of the 2011 IEEE Pacific Visualization Symposium, PACIFICVIS ‘11, pages 187-194, Washington, DC, USA, 2011. IEEE Computer Society. - [13] E. R. Gansner, Y. Koren, and S. C. North., Topological fisheye views for visualizing large graphs
IEEE Transactions on Visualization and Computer Graphics, 11(4): 457-468, July 2005.- [14] D. Holten, Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data
IEEE Transactions on Visualization and Computer Graphics, 12: 2006, 2006.- [15] D. Holten and J. J. Van Wijk., Force-directed edge bundling for graph visualization
Computer Graphics Forum, 28(3): 983-990, 2009.- [16] Y. F. Hu., Efficient and high quality force-directed graph drawing
The Mathematica Journal, 10: 37-71, 2005.- [17] C. Hurter, O. Ersoy, and A. Telea, Graph bundling by kernel density estimation
Computer Graphics Forum (EuroVis 2012), 31(3): 865-874, 2012.- [18] D. A. Keirn,M. C. Hao, U. Dayal, H. Janetzko,, and P. Bak., Generalized scatter plots
Information Visualization, 9: 301-311, December 2010.- [19] A. Lambert, R. Bourqui, and D. Auber, Winding roads: Routing edges into bundles
Computer Graphics Forum, 29(3): 853-862, 2010.- [20] O. D. Lampe and H. Hauser., Interactive visualization of streaming data with kernel density estimation. In
Proc. IEEE Pacific Visualization Symp. (PacificVis), pages 171-178, 2011.- [21] D. Phan, L. Xiao, R. Yeh., P. Hanrahan, and T. Winograd., Flow Map Layout. Proceedings of the 2005 IEEE Symposium on Information Visualization, 0:29+, 2005.
- [22] A. Quigley and P. Eades., FADE: Graph Drawing, Clustering, and Visual Abstraction. In
GD ‘00: Proceedings of the 8th International Symposium on Graph Drawing, pages 197-210, London, UK, 2001. Springer-Verlag. - [23] H. Samet, The quadtree and related hierarchical data structures
ACM Comput. Surv., 16: 187-260, June 1984.- [24] M. Sarkar and M. H. Brown., Graphical fisheye views of graphs. In
Proceedings of the SIGCHI conference on Human factors in computing systems, CHI ‘92, pages 83-91, New York, NY, USA, 1992. ACM. - [25] B. Silverman.,
Density estimation for statistics and data analysis. Mono-graphs on statistics and applied probability. Chapman and Hall, 1986.- [26] A. Telea and O. Ersoy, Image-based edge bundles: Simplified visualization of large graphs
Computer Graphics Forum, 29(3): 843-852, 2010.- [27] U.S. Census Bureau. County-to-county migration flow files. http://www.census.gov/population/www/cen2000/ ctytoctyflow, June 2012.
- [28] R. van Liere and W. de Leeuw., Graphsplatting: Visualizing graphs as continuous fields.
IEEE Transactions on Visualization and Computer Graphics, 9(2): 206-212, Apr. 2003. |