Efficient space virtualization for the Hoshen-Kopelman algorithm

In this paper, the efficient space virtualisation for the Hoshen-Kopelman algorithm is presented. We observe minimal parallel overhead during computations, due to negligible communication costs. The proposed algorithm is applied for computation of random-site percolation thresholds for four dimensional simple cubic lattice with sites' neighborhoods containing next-next-nearest neighbors (3NN). The obtained percolation thresholds are p(C)(NN) = 0.19680(23), p(C)(2NN) =0.08410(23), p(C)(3NN)=0.04540(23), p(C)(2NN+NN)=0.06180(23), p(C)(3NN+NN) = 0.04000(23), p(C)(3NN + 2NN) = 0.03310(23), p(C)(3NN + 2NN + NN) = 0.03190(23), where 2NN and NN stand for next-nearest neighbors and nearest neighbors, respectively.