CUBu: Universal Real-Time Bundling for Large Graphs

Visualizing very large graphs by edge bundling is a promising method, yet subject to several challenges: speed, clutter, level-of-detail, and parameter control. We present CUBu, a framework that addresses the above problems in an integrated way. Fully GPU-based, CUBu bundles graphs of up to a million edges at interactive framerates, being over 50 times faster than comparable state-of-the-art methods, and has a simple and intuitive control of bundling parameters. CUBu extends and unifies existing bundling techniques, offering ways to control bundle shapes, separate bundles by edge direction, and shade bundles to create a level-of-detail visualization that shows both the graph core structure and its details. We demonstrate CUBu on several large graphs extracted from real-life application domains.

[1]  Michel Barlaud,et al.  Fast k nearest neighbor search using GPU , 2008, 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[2]  Christophe Hurter,et al.  Attribute-driven edge bundling for general graphs with applications in trail analysis , 2015, 2015 IEEE Pacific Visualization Symposium (PacificVis).

[3]  Romain Bourqui,et al.  3D Edge Bundling for Geographical Data Visualization , 2010, 2010 14th International Conference Information Visualisation.

[4]  Jarke J. van Wijk,et al.  Interactive Visualization of Small World Graphs , 2004, IEEE Symposium on Information Visualization.

[5]  Peter Eades,et al.  StreamEB: Stream Edge Bundling , 2012, Graph Drawing.

[6]  Christophe Hurter,et al.  Skeleton-Based Edge Bundling for Graph Visualization , 2011, IEEE Transactions on Visualization and Computer Graphics.

[7]  Ulrik Brandes,et al.  Interactive Level-of-Detail Rendering of Large Graphs , 2012, IEEE Transactions on Visualization and Computer Graphics.

[8]  Sergey Bereg,et al.  Edge Routing with Ordered Bundles , 2011, Graph Drawing.

[9]  Guy Melançon,et al.  Multiscale visualization of small world networks , 2003, IEEE Symposium on Information Visualization 2003 (IEEE Cat. No.03TH8714).

[10]  Jarke J. van Wijk,et al.  Cushion Treemaps: Visualization of Hierarchical Information , 1999, INFOVIS.

[11]  Romain Bourqui,et al.  Winding Roads: Routing edges into bundles , 2010, Comput. Graph. Forum.

[12]  Robert van Liere,et al.  GraphSplatting: Visualizing Graphs as Continuous Fields , 2003, IEEE Trans. Vis. Comput. Graph..

[13]  Martin Wattenberg,et al.  Centrality Based Visualization of Small World Graphs , 2008, Comput. Graph. Forum.

[14]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Alan J. Dix,et al.  A Taxonomy of Clutter Reduction for Information Visualisation , 2007, IEEE Transactions on Visualization and Computer Graphics.

[16]  Alexandru Telea,et al.  Data visualization - principles and practice , 2007 .

[17]  Christophe Hurter,et al.  MoleView: An Attribute and Structure-Based Semantic Lens for Large Element-Based Plots , 2011, IEEE Transactions on Visualization and Computer Graphics.

[18]  A. Asuncion,et al.  UCI Machine Learning Repository, University of California, Irvine, School of Information and Computer Sciences , 2007 .

[19]  Stephan Diehl,et al.  Software Visualization - Visualizing the Structure, Behaviour, and Evolution of Software , 2007 .

[20]  Alexandru Telea,et al.  Eurographics/ Ieee-vgtc Symposium on Visualization 2010 Image-based Edge Bundles: Simplified Visualization of Large Graphs , 2022 .

[21]  Cláudio T. Silva,et al.  Two-Phase Mapping for Projecting Massive Data Sets , 2010, IEEE Transactions on Visualization and Computer Graphics.

[22]  Yifan Hu,et al.  Multilevel agglomerative edge bundling for visualizing large graphs , 2011, 2011 IEEE Pacific Visualization Symposium.

[23]  Gennady L. Andrienko,et al.  Composite Density Maps for Multivariate Trajectories , 2011, IEEE Transactions on Visualization and Computer Graphics.

[24]  Daniel S. Margulies,et al.  Three-Dimensional Mean-Shift Edge Bundling for the Visualization of Functional Connectivity in the Brain , 2012, IEEE Transactions on Visualization and Computer Graphics.

[25]  Christophe Hurter,et al.  FromDaDy: Spreading Aircraft Trajectories Across Views to Support Iterative Queries , 2009, IEEE Transactions on Visualization and Computer Graphics.

[26]  Charl P. Botha,et al.  Piece wise Laplacian‐based Projection for Interactive Data Exploration and Organization , 2011, Comput. Graph. Forum.

[27]  Arie van Deursen,et al.  Execution trace analysis through massive sequence and circular bundle views , 2008, J. Syst. Softw..

[28]  Alexander Wolff,et al.  Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming , 2011, IEEE Transactions on Visualization and Computer Graphics.

[29]  Luis Gustavo Nonato,et al.  Local Affine Multidimensional Projection , 2011, IEEE Transactions on Visualization and Computer Graphics.

[30]  Philippe Caisso ADS - B (Automatic Dependent Surveillance - Broadcast) , 2001 .

[31]  Hong Zhou,et al.  Geometry-Based Edge Clustering for Graph Visualization , 2008, IEEE Transactions on Visualization and Computer Graphics.

[32]  Matthias Zwicker,et al.  Ieee Transactions on Visualization and Computer Graphics Ewa Splatting , 2002 .

[33]  Alexandru Telea,et al.  Dynamic multiscale visualization of flight data , 2015, 2014 International Conference on Computer Vision Theory and Applications (VISAPP).

[34]  Christophe Hurter,et al.  Graph Bundling by Kernel Density Estimation , 2012, Comput. Graph. Forum.

[35]  Alexandru C. Telea Data Visualization: Principles and Practice, Second Edition , 2014 .

[36]  Stephen G. Walker,et al.  Automatic Metro Map Layout Using Multicriteria Optimization , 2011, IEEE Transactions on Visualization and Computer Graphics.

[37]  Tiow Seng Tan,et al.  Parallel Banding Algorithm to compute exact distance transform with the GPU , 2010, I3D '10.

[38]  Cláudio T. Silva,et al.  User-Centered Multidimensional Projection Techniques , 2012, Computing in Science & Engineering.

[39]  Jarke J. van Wijk,et al.  Force‐Directed Edge Bundling for Graph Visualization , 2009, Comput. Graph. Forum.

[40]  Helwig Hauser,et al.  Interactive visualization of streaming data with Kernel Density Estimation , 2011, 2011 IEEE Pacific Visualization Symposium.

[41]  Richard Boardman Bubble trees the visualization of hierarchical information structures , 2000, CHI Extended Abstracts.

[42]  Christophe Hurter,et al.  Bundled Visualization of DynamicGraph and Trail Data , 2014, IEEE Transactions on Visualization and Computer Graphics.

[43]  Rosane Minghim,et al.  Visual analysis of dimensionality reduction quality for parameterized projections , 2014, Comput. Graph..

[44]  Busyairah Syd Ali,et al.  Automatic Dependent Surveillance Broadcast (ADS-B) , 2017 .

[45]  Lucian Voinea,et al.  The Solid* toolset for software visual analytics of program structure and metrics comprehension: From research prototype to product , 2014, Sci. Comput. Program..

[46]  Christophe Hurter,et al.  Interactive image-based information visualization for aircraft trajectory analysis , 2014 .

[47]  Haim Levkowitz,et al.  Least Square Projection: A Fast High-Precision Multidimensional Projection Technique and Its Application to Document Mapping , 2008, IEEE Transactions on Visualization and Computer Graphics.

[48]  Danny Holten,et al.  Hierarchical Edge Bundles: Visualization of Adjacency Relations in Hierarchical Data , 2006, IEEE Transactions on Visualization and Computer Graphics.

[49]  Hong Zhou,et al.  Edge bundling in information visualization , 2013 .

[50]  John Dingliana,et al.  An empirical study on the impact of edge bundling on user comprehension of graphs , 2012, AVI.

[51]  Peter Eades,et al.  TGI-EB: A New Framework for Edge Bundling Integrating Topology, Geometry and Importance , 2011, Graph Drawing.

[52]  Jeffrey Heer,et al.  Divided Edge Bundling for Directional Network Data , 2011, IEEE Transactions on Visualization and Computer Graphics.

[53]  Lawrence Cayton,et al.  A Nearest Neighbor Data Structure for Graphics Hardware , 2010, ADMS@VLDB.

[54]  Hong Zhou,et al.  Visual Clustering in Parallel Coordinates , 2008, Comput. Graph. Forum.

[55]  Alexandru Telea,et al.  Extraction and visualization of call dependencies for large C/C++ code bases: A comparative study , 2009, 2009 5th IEEE International Workshop on Visualizing Software for Understanding and Analysis.

[56]  Daniel C. Moura,et al.  3D Density Histograms for Criteria-driven Edge Bundling , 2015, ArXiv.

[57]  Joel Wichgers Automatic Dependent Surveillance—Broadcast , 2014 .