Faster force-directed graph drawing with the well-separated pair decomposition (Q1736822)

Summary: The force-directed paradigm is one of the few generic approaches to drawing graphs. Since force-directed algorithms can be extended easily, they are used frequently. Most of these algorithms are, however, quite slow on large graphs, as they compute a quadratic number of forces in each iteration. We give a new algorithm that takes only \(O(m+n\log n)\) time per iteration when laying out a graph with \(n\) vertices and \(m\) edges. Our algorithm approximates the true forces using the so-called well-separated pair decomposition. We perform experiments on a large number of graphs and show that we can strongly reduce the runtime, even on graphs with less than a hundred vertices, without a significant influence on the quality of the drawings (in terms of the number of crossings and deviation in edge lengths).