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.
Goldsmith et al. REF researched the computational complexity of testing dominance and consistency in CP-nets, and proved that both dominance and consistency for general CP-nets are PSPACE-complete.
The Computational Complexity of Dominance and Consistency in CP-Nets
Journal Of Artificial Intelligence Research, Volume 33, pages 403-432, 2008
Computer Science Mathematics