Efficient space virtualisation for Hoshen--Kopelman algorithm
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In this paper the efficient space virtualisation for 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' neighbourhoods containing next-next-nearest neighbours (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 neighbours and nearest neighbours, respectively.
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