Exact Dominance Querying Algorithm on CP-nets

Abstract

CP-nets (conditional preference networks) is a graphical model for representing qualitative conditional preference statements via ceteris paribus semantics interpretation. Dominance querying, the problem of determining whether an outcome is preferred to another on this graphical model, is of fundamental importance in preference querying. However, to date, the exact dominance querying algorithm with respect to any binaryvalued CP-nets has not been given, hence designing an exact dominance querying algorithm is quite necessary. Fortunately, we discover that dominance querying problem is essentially a single source shortest path problem, and the induced graph of CP-nets is a sparse graph, as a result, dominance querying problem can be solved by Johnson algorithm which is suitable for solving the single source shortest path problem on sparse graph. As a byproduct, this algorithm can determine least flip numbers if an outcome dominates another outcome. At last, we present results of experiments that demonstrate the feasibility of our approach to dominance querying on acyclic CP-nets.