| Abstract: | This paper proposes a linear‐time repulsive‐force‐calculation algorithm with sub‐linear auxiliary space requirements, achieving an asymptotic improvement over the Barnes‐Hut and Fast Multipole Method force‐calculation algorithms. The algorithm, named random vertex sampling (RVS), achieves its speed by updating a random sample of vertices at each iteration, each with a random sample of repulsive forces. This paper also proposes a combination algorithm that uses RVS to derive an initial layout and then applies Barnes‐Hut to refine the layout. An evaluation of RVS and the combination algorithm compares their speed and quality on 109 graphs against a Barnes‐Hut layout algorithm. The RVS algorithm performs up to 6.1 times faster on the tested graphs while maintaining comparable layout quality. The combination algorithm also performs faster than Barnes‐Hut, but produces layouts that are more symmetric than using RVS alone. Data and code: https://osf.io/nb7m8/ |
