Hierarchical graph maps

Abstract Graphs and maps are powerful abstractions. Their combination, Hierarchical Graph Maps, provide effective tools to process a graph that is too large to fit on the screen. They provide hierarchical visual indices (i.e. maps) that guide navigation and visualization. Hierarchical graph maps deal in a unified manner with both the screen and I/O bottlenecks. This line of thinking adheres to the Visual Information Seeking Mantra: Overview first, zoom and filter, then details on demand (Information Visualization: dynamic queries, star field displays and lifelines, in www.cr.umd.edu, 1997). We highlight the main tasks behind the computation of Graph Maps and provide several examples. The techniques have been used experimentally in the navigation of graphs defined on vertex sets ranging from 100 to 250 million vertices.

[1]  Kozo Sugiyama,et al.  Visualization of structural information: automatic drawing of compound digraphs , 1991, IEEE Trans. Syst. Man Cybern..

[2]  James Abello,et al.  Navigating Giga-Graphs , 2002, AVI '02.

[3]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[4]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[5]  Michael T. Goodrich,et al.  A multi-dimensional approach to force-directed layouts of large graphs , 2000, Comput. Geom..

[6]  James Abello,et al.  Navigating Graph Surfaces , 2000 .

[7]  Michael T. Goodrich,et al.  Balanced Aspect Ratio Trees and Their Use for Drawing Very Large Graphs , 1998, GD.

[8]  James Abello,et al.  Hierarchical graph indexing , 2003, CIKM '03.

[9]  Irene Finocchi,et al.  Graph sketches , 2001, IEEE Symposium on Information Visualization, 2001. INFOVIS 2001..

[10]  P. M. Pardalos,et al.  Approximation and Complexity in Numerical Optimization: Continuous And Discrete Problems , 2006 .

[11]  James Abello,et al.  MGV: A System for Visualizing Massive Multidigraphs , 2002, IEEE Trans. Vis. Comput. Graph..

[12]  Peter Eades,et al.  Multilevel Visualization of Clustered Graphs , 1996, GD.

[13]  Michael T. Goodrich,et al.  A Multi-dimensional Approach to Force-Directed Layouts of Large Graphs , 2000, Graph Drawing.

[14]  Vijay Kumar,et al.  Improved algorithms and data structures for solving graph problems in external memory , 1996, Proceedings of SPDP '96: 8th IEEE Symposium on Parallel and Distributed Processing.

[15]  Stefan Jeschke,et al.  General Rectangular FishEye Views for 2 , 2000 .

[16]  Jeffery R. Westbrook,et al.  A Functional Approach to External Graph Algorithms , 1998, ESA.

[17]  Xuemin Lin,et al.  Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs , 1996, Graph Drawing.