CP-nets - Reasoning and Consistency Testing

Preference elicitation and preference representation play an important role in any effort to automate decision making. Unfortunately, few tools exist for preference elicitation that allow the decision maker to conveniently structure its preferences and the decision engine to efficiently reason about these preferences. One of the only such tools is CP-nets, which use a graphical representation that is superficially similar to Bayesian networks. Despite a number of interesting applications, most of the major theoretical questions related to CP-nets remain open. In particular, the complexity of determining whether one outcome is preferred to another outcome (dominance testing) is known for tree-structured networks only; moreover, little is known about the consistency of cyclic CP-nets. In this paper we show how the complexity of dominance testing depends on the structure of the CP-net. In particular we provide a new polynomial time algorithm for poly trees. In addition, we show a class of cyclic CP-nets that is never consistent, while other classes on which consistency can be tested for efficiently.