The cluster algorithms are very different to Metropolis. The main computational task is to take local information (bond connections) and work out global information (clusters of sites).
This is an example of connected component labeling, which is a standard graph problem --- given a graph of vertices and edges, the problem is to identify those vertices which form a connected set, where a vertex is in the set if it has an edge connecting it to another vertex in the set. For cluster algorithms, the vertices are the lattice sites, the edges are the bonds, and the connected components are the clusters.
Component labeling is commonly used in image processing, to join neighboring pixels into connected regions which are the shapes in the image. Efficient sequential algorithms exist for this procedure, however implementing an efficient parallel algorithm is difficult.