A general polynomial-time framework finds stable matchings that minimize utilitarian or egalitarian objectives for any polynomial-time computable set functions by reducing them to linear edge weights.
Stable matchings, optimal assignments, and linear programming
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Maximally Diverse Stable Matchings: Optimizing Arbitrary Institutional Objectives
A general polynomial-time framework finds stable matchings that minimize utilitarian or egalitarian objectives for any polynomial-time computable set functions by reducing them to linear edge weights.