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

Abstract 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.

[1]  Yutaka Okabe,et al.  GPU-based Swendsen-Wang multi-cluster algorithm for the simulation of two-dimensional classical spin systems , 2012, Comput. Phys. Commun..

[2]  Wolfgang Paul,et al.  GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model , 2009, J. Comput. Phys..

[3]  M. Weigel.  Connected-component identification and cluster update on graphics processing units. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[5]  Kenneth A. Hawick,et al.  Parallel graph component labelling with GPUs and CUDA , 2010, Parallel Comput..

[6]  Raoul Kopelman,et al.  Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm , 1976 .

[7]  L. Onsager.  Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[8]  Wolff,et al.  Collective Monte Carlo updating for spin systems. , 1989, Physical review letters.

[9]  Alan M. Ferrenberg,et al.  Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study. , 1991, Physical review. B, Condensed matter.

[10]  Erik Luijten,et al.  Ising universality in three dimensions: a Monte Carlo study , 1995, cond-mat/9509016.

[11]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[12]  Yutaka Okabe,et al.  Multi-GPU-based Swendsen-Wang multi-cluster algorithm for the simulation of two-dimensional q-state Potts model , 2012, Comput. Phys. Commun..

[13]  Thomas Steinke,et al.  Swendsen-Wang multi-cluster algorithm for the 2D/3D Ising model on Xeon Phi and GPU , 2013, 2013 SC - International Conference for High Performance Computing, Networking, Storage and Analysis (SC).

[14]  Ralf Schneider,et al.  Connected component labeling on a 2D grid using CUDA , 2011, J. Parallel Distributed Comput..

[15]  Clive F. Baillie,et al.  Cluster Identification Algorithms for Spin Models - Sequential and Parallel , 1991, Concurr. Pract. Exp..