An Evolutionary Algorithm for an Optimization Model of Edge Bundling

This paper presents two edge bundling optimization problems that address minimizing the total number of bundles, in conjunction with other aspects, as the main goal. A novel evolutionary edge bundling algorithm for these problems is described. The algorithm was successfully tested by solving two related problems applied to real-world instances in reasonable computational time. The development and analysis of optimization models have received little attention in the area of edge bundling. However, the reported experimental results demonstrate the effectiveness and the applicability of the proposed evolutionary algorithm to help resolve edge bundling problems formally defined as optimization models.

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

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

[3]  Rebecca Linda McKnight.  Low-stretch trees for network visualization , 2015 .

[4]  Ulrik Brandes,et al.  Stub Bundling and Confluent Spirals for Geographic Networks , 2013, GD.

[5]  Wei Chen,et al.  SideKnot: Revealing relation patterns for graph visualization , 2012, 2012 IEEE Pacific Visualization Symposium.

[6]  Alexander Wolff,et al.  Progress on Partial Edge Drawings , 2012, GD.

[7]  Michael A. Bekos,et al.  1-Fan-Bundle-Planar Drawings of Graphs , 2017, GD.

[8]  Michael Kaufmann,et al.  Improving Layered Graph Layouts with Edge Bundling , 2010, GD.

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

[10]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[11]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Donald E. Knuth,et al.  The Stanford GraphBase - a platform for combinatorial computing , 1993 .

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

[14]  Ryosuke Saga.  Quantitative Evaluation for Edge Bundling by Difference of Edge Lengths and Area Occupation , 2016, HCI.

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

[16]  Christophe Hurter,et al.  State of the Art in Edge and Trail Bundling Techniques , 2017, Comput. Graph. Forum.

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

[18]  Steven Skiena,et al.  Implementing discrete mathematics - combinatorics and graph theory with Mathematica , 1990 .

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

[20]  Muhammad Jawaherul Alam,et al.  The Bundled Crossing Number , 2016, GD.

[21]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[22]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[23]  Saroj.  A Non-Revisiting Genetic Algorithm for Optimizing Numeric Multi-Dimensional Functions , 2012 .