[*next nearest neighbor (NNN)*]{} sites [@gtg]. We find that this [*NNN*]{} hopping algorithm is particularly effective in terms of simulation time as compared with [*NN*]{} hopping alone, as was emphasized in [@gtg]. Moreover, at low temperature, [*NN*]{} hopping alone presented severe energy barriers to the motions of charges in the case of relatively dense Coulomb gas, [*i.e.*]{}, $f$ approximately larger than $1/3$.

The presented results are averages over $100 \sim 500$ different random initial configurations depending on the temperature. In order to ensure that equilibration is achieved, we calculate the two-time charge density autocorrelation function and locate the waiting time beyond which the autocorrelation function no longer depends on the waiting time. As for the values of the charge density parameter $f$, we chose $f = 55/144 \simeq 0.3819$ that is close to $f=1-g$, and square lattices of linear size $L=36$ is chosen with periodic boundary conditions. This value of $f$ is chosen as a simple rational value that satisfies the two conditions of both being close to $1-g$ and being commensurate with the lattice periodicity $12$ as explained in Section III. We found that qualitative features of relaxation dynamics are the same for other nearby values of the frustration 