GPU-based cluster-labeling algorithm without the use of conventional iteration: Application to the Swendsen-Wang multi-cluster spin flip algorithm

Cluster-labeling algorithms that use a single GPU can be roughly divided into direct and two-stage approaches. To date, both types use an iterative method to compare the labels of nearest-neighbor sites. In this paper, I present a GPU-based cluster-labeling algorithm that does not use conventional iteration. The proposed method is applicable to both direct algorithms and two-stage approaches. Under the proposed approach, only one comparison with the nearest-neighbor site is needed for a two-dimensional (2D) system, and just two comparisons are needed for three-dimensional (3D) systems. As an application of the new cluster-labeling algorithm, I consider the Swendsen-Wang (SW) multi-cluster spin flip algorithm. The performance of the proposed method is compared with that of other cluster-labeling algorithms for the SW multi-cluster spin flip problem using the 2D and 3D Ising models. As a result, the computation time of the new algorithm is shown to be 40% faster than that of the previous algorithm for the 2D Ising model, and 20% faster than that of the previous algorithm for the 3D Ising model at the critical temperature.