Kidney Exchange over the Blood Group Barrier

This paper investigates a pairwise kidney exchange program that includes patient-donor pairs in which the patients can receive a kidney across the blood group barrier from their own donors. Patients in such pairs gain strictly by an exchange if they are matched to a fully compatible donor. We study the set of priority matchings where the number of patients matched to fully compatible donors is maximized among all priority matchings and where all matched patients that can receive a kidney across the blood group barrier from their own donors are matched to fully compatible donors. The main result demonstrates that matchings in this set can be identified by solving an appropriately defined maximum weight matching problem. It is also demonstrated that the inclusion of patients that can receive a kidney across the blood group barrier from their own donors will not reduce the number of transplants for patients with incompatible donors, as all patients involved in an exchange before the inclusion are still involved in an exchange after the inclusion