A Divide and Conquer Algorithm for Dominance Testing in Acyclic CP-Nets

The Conditional Preference Network (CP-net) represents user's conditional ceteris paribus (all else being equal) preference statements in a graphical manner. In general, an acyclic CP-net induces a strict partial order over the outcomes. The task of comparing two outcomes (dominance testing) is generally PSPACE-complete, which is a limitation for this intuitive model, especially when representing and solving preference-based constrained optimization problems. In order to overcome this limitation in practice, we propose a divide and conquer algorithm that compares two outcomes according to dominance testing. The algorithm divides the original CP-net into sub CP-nets, and recursively calls itself for each of the sub CP-nets until it reaches to a termination criterion. In the termination criterion, the answer of the dominance query is returned. With a theoretical analysis of the time performance, we demonstrate that the proposed algorithm outperforms the existing methods.