Compact Preference Representation in Stable Marriage Problems

The stable marriage problem has many practical applications in two-sided markets like those that assign doctors to hospitals, students to schools, or buyers to vendors. Most algorithms to find stable marriages assume that the participants explicitly expresses a preference ordering. This can be problematic when the number of options is large or has a combinatorial structure. We consider therefore using CP-nets, a compact preference formalism in stable marriage problems. We study the impact of this formalism on the computational complexity of stable marriage procedures, as well as on the properties of the solutions computed by these procedures. We show that it is possible to model preferences compactly without significantly increasing the complexity of stable marriage procedures and whilst maintaining the desirable properties of the matching returned.