Efficient space virtualisation for Hoshen--Kopelman algorithm

TL;DR

This paper introduces an efficient space virtualisation technique for the Hoshen--Kopelman algorithm, enabling minimal parallel overhead and application to compute percolation thresholds in four-dimensional lattices with various neighbor configurations.

Contribution

The paper presents a novel space virtualisation method for the Hoshen--Kopelman algorithm, reducing communication costs and demonstrating its effectiveness in calculating percolation thresholds in complex 4D lattices.

Findings

Minimal parallel overhead observed during computations.

Accurate percolation thresholds obtained for various neighbor configurations.

Method applicable to high-dimensional lattice percolation problems.

Abstract

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 $p_C(\text{NN})=0.19680(23)$, $p_C(\text{2NN})=0.08410(23)$, $p_C(\text{3NN})=0.04540(23)$, $p_C(\text{2NN+NN})=0.06180(23)$, $p_C(\text{3NN+NN})=0.04000(23)$, $p_C(\text{3NN+2NN})=0.03310(23)$, $p_C(\text{3NN+2NN+NN})=0.03190(23)$, where 2NN and NN stand for next-nearest neighbours and nearest neighbours, respectively.