The Computational Complexity of Dominance and Consistency in CP-Nets
This work addresses foundational complexity issues in AI for researchers in preference reasoning, but it is incremental as it extends prior results from acyclic to cyclic cases.
The paper tackled the computational complexity of testing dominance and consistency in general CP-nets, which model preferences with cyclic dependency graphs, and showed that these problems are PSPACE-complete.
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.