  We present the GPU calculation with the common unified device architecture
(CUDA) for the Swendsen-Wang multi-cluster algorithm of two-dimensional
classical spin systems. We adjust the two connected component labeling
algorithms recently proposed with CUDA for the assignment of the cluster in the
Swendsen-Wang algorithm. Starting with the q-state Potts model, we extend our
implementation to the system of vector spins, the q-state clock model, with the
idea of embedded cluster. We test the performance, and the calculation time on
GTX580 is obtained as 2.51 nano sec per a spin flip for the q=2 Potts model
(Ising model) and 2.42 nano sec per a spin flip for the q=6 clock model with
the linear size L=4096 at the critical temperature, respectively. The
computational speed for the q=2 Potts model on GTX580 is 12.4 times as fast as
the calculation speed on a current CPU core. That for the q=6 clock model on
GTX580 is 35.6 times as fast as the calculation speed on a current CPU core.
