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 pC(NN)=0.19680(23), pC(2NN)=0.08410(23), pC(3NN)=0.04540(23), pC(2NN+NN)=0.06180(23), pC(3NN+NN)=0.04000(23), pC(3NN+2NN)=0.03310(23), pC(3NN+2NN+NN)=0.03190(23), where 2NN and NN stand for next-nearest neighbors and nearest neighbors, respectively.