Cluster counting: The Hoshen-Kopelman algorithm vs. spanning tree approaches

TL;DR

This paper compares the Hoshen-Kopelman algorithm and spanning tree methods for cluster counting in percolation models, discussing their modifications, parallelization, and applications to backbone extraction.

Contribution

It provides a detailed comparison and implementation insights for cluster counting algorithms, including modifications and graph-theoretical approaches.

Findings

Hoshen-Kopelman algorithm is redescribed and extended for various lattices.

Spanning tree approaches using BFS and DFS are explained with examples.

Implementation of the pebble game algorithm using DFS is described.

Abstract

Two basic approaches to the cluster counting task in the percolation and related models are discussed. The Hoshen-Kopelman multiple labeling technique for cluster statistics is redescribed. Modifications for random and aperiodic lattices are sketched as well as some parallelised versions of the algorithm are mentioned. The graph-theoretical basis for the spanning tree approaches is given by describing the "breadth-first search" and "depth-first search" procedures. Examples are given for extracting the elastic and geometric "backbone" of a percolation cluster. An implementation of the "pebble game" algorithm using a depth-first search method is also described.