Uncluttering graph layouts using anisotropic diffusion and mass transport

Many graph layouts include very dense areas, making the layout difficult to understand. In this paper, we propose a technique for modifying an existing layout in order to reduce the clutter in dense areas. A physically inspired evolution process based on a modified heat equation is used to create an improved layout density image, making better use of available screen space. Using results from optimal mass transport problems, a warp to the improved density image is computed. The graph nodes are displaced according to the warp. The warp maintains the overall structure of the graph, thus limiting disturbances to the mental map, while reducing the clutter in dense areas of the layout. The complexity of the algorithm depends mainly on the resolution of the image visualizing the graph and is linear in the size of the graph. This allows scaling the computation according to required running times. It is demonstrated how the algorithm can be significantly accelerated using a graphics processing unit (GPU), resulting in the ability to handle large graphs in a matter of seconds. Results on several layout algorithms and applications are demonstrated.