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 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.  
