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Couples can be tractable: New algorithms and hardness results for the Hospitals / Residents problem with Couples
We present a novel polynomial-time algorithm that can find a near-feasible stable matching (adjusting the hospitals' capacities by at most 1) in an {\sc hrc} instance where the couples' preferences are sub-responsive (i. e., if one member switches to a better hospital, than the couple also improves) and sub-complete (i. e., each pair of hospitals that are individually acceptable to both members are jointly acceptable for the couple) by reducing it to an instance of the {\sc Stable Fixtures} problem.
Position-Indexed Formulations for Kidney Exchange
The recent introduction of chains, where a donor without a paired patient triggers a sequence of donations without requiring a kidney in return, increased the efficacy of fielded kidney exchanges---while also dramatically raising the empirical computational hardness of clearing the market in practice.
