First proposed by Fisher and Galler, implemented in a more efficient manner by Hoshen and Kopelmann for percolation studies.
Uses the idea of a rooted tree. Each site has a pointer to another site in the cluster, and so on down a tree-like structure. The site that is the root of the tree has the label for the cluster. Sites find their labels by traversal of the tree. Periodically pruning the tree (making shortcuts) makes the algorithm efficient.
The breadth-first search is better suited to a parallelism than the depth-first search, since it involves an outer loop over all sites, which can be parallelized using standard domain decomposition.