  We investigate the computational complexity of testing dominance and
consistency in CP-nets. Previously, the complexity of dominance has been
determined for restricted classes in which the dependency graph of the CP-net
is acyclic. However, there are preferences of interest that define cyclic
dependency graphs; these are modeled with general CP-nets. In our main results,
we show here that both dominance and consistency for general CP-nets are
PSPACE-complete. We then consider the concept of strong dominance, dominance
equivalence and dominance incomparability, and several notions of optimality,
and identify the complexity of the corresponding decision problems. The
reductions used in the proofs are from STRIPS planning, and thus reinforce the
earlier established connections between both areas.
