NP-Completeness of Outcome Optimization for Partial CP-Nets

CP-nets (Boutilier 2004) represent qualitative conditional preferences using a graphical model similar in concept to a belief network. A CP-net describes the preferences over the values of each problem variable, possibly conditioned on the values of other variables. For example, a user might describe her ideal dinner by expressing an (unconditional) preference for a meat entrée over a fish entrée, and a preference for wine that depends on the particular choice of entrée (red wine with meat, and white wine with fish). The CP-net for this diner would look like the one in Figure 1, with the exception that a preference would be expressed for the value of D. CP-nets make it easy to find the most preferred meal using a linear forward sweep algorithm. First, a meat entrée is selected based on the unconditional preference. Then, wine is selected to match the choice of entrée: red in this example.