Hachul, Stefan and Jünger, Michael (2005) Large-Graph Layout with the Fast Multipole Multilevel Method.
Technical Report , 27 p.

Abstract

The visualization of of large and complex networks or graphs is an indispensable instrument for getting deeper insight into their structure. Force-directed graph-drawing algorithms are widely used to draw such graphs. However, these methods do not guarantee a sub-quadratic running time in general. We present a new force-directed method that is based on a combination of an efficient multilevel scheme and a strategy for approximating the repulsive forces in the system by rapidly evaluating potential fields. Given a graph G=(V,E), the asymptotic worst-case running time of this method is O(|V|log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs with 100000 nodes in less than 5 minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other methods.

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