“…Given a CP-net, complexity issue is to determine the computational complexities of some query tasks, such as dominance test (checking whether an outcome is preferred to another one, that is, whether N o 1 1 o 2 is true [14]), outcome optimization query [3,27] (solving the best outcomes, that is, we look for the most preferable outcomes from outcome space X), skyline query [1] (determining outcomes which are not dominated by any other outcomes), and other query tasks as described in literature [22]. Indeed, all these query tasks can be perceived as reasoning tasks on graphical model, the complexity perspective is concerned with devising effective query algorithms for solving these reasoning tasks.…”