The first approach is to extend the bond-formation rules to more non-local cells, and the second approach is to generate clusters based on more relevant order parameters. In the first case, we have the KBD algorithm for the fully-frustrated Ising model, where the decision of opening bonds are made on each plaquette, arranged in a checkerboard pattern on the square lattice. In the second case, we have replica cluster move for low-dimensional spin glasses, where the clusters are generated based on spin overlaps, which is believed to be the relevant order parameter.