  Standard Monte Carlo cluster algorithms have proven to be very effective for
many different spin models, however they fail for frustrated spin systems.
Recently a generalized cluster algorithm was introduced that works extremely
well for the fully frustrated Ising model on a square lattice, by placing bonds
between sites based on information from plaquettes rather than links of the
lattice. Here we study some properties of this algorithm and some variants of
it. We introduce a practical methodology for constructing a generalized cluster
algorithm for a given spin model, and investigate apply this method to some
other frustrated Ising models. We find that such algorithms work well for
simple fully frustrated Ising models in two dimensions, but appear to work
poorly or not at all for more complex models such as spin glasses.
