An Evolutionary Algorithm for an Optimization Model of Edge Bundling

This paper discusses three edge bundling optimization problems that aim to minimize the total number of bundles of a graph drawing, in conjunction with other aspects, as the main goal. A novel evolutionary algorithm for edge bundling for these problems is described. The algorithm was successfully tested by solving the 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 by formally defining them as optimization models.

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

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

[3]  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.

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

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

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

[7]  Christophe Hurter,et al.  Functional Decomposition for Bundled Simplification of Trail Sets , 2018, IEEE Transactions on Visualization and Computer Graphics.

[8]  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.

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

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

[11]  V. M. Abraham,et al.  Decomposition of Graphs into Paths and Cycles , 2013 .

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

[13]  Konstantin Avrachenkov,et al.  Cooperative Game Theory Approaches for Network Partitioning , 2017, COCOON.

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

[15]  Kwan-Liu Ma,et al.  Ambiguity-Free Edge-Bundling for Interactive Graph Visualization , 2012, IEEE Transactions on Visualization and Computer Graphics.