Optimizing kidney exchange with transplant chains: theory and reality

Kidney exchange, where needy patients swap incompatible donors with each other, offers a lifesaving alternative to waiting for an organ from the deceased-donor waiting list. Recently, chains— sequences of transplants initiated by an altruistic kidney donor— have shown marked success in practice, yet remain poorly understood. We provide a theoretical analysis of the efficacy of chains in the most widely used kidney exchange model, proving that long chains do not help beyond chains of length of 3 in the large. This completely contradicts our real-world results gathered from the budding nationwide kidney exchange in the United States; there, solution quality improves by increasing the chain length cap to 13 or beyond. We analyze reasons for this gulf between theory and practice, motivated by our experiences running the only nationwide kidney exchange. We augment the standard kidney exchange model to include a variety of real-world features. Experiments in the static setting support the theory and help determine how large is really “in the large". Experiments in the dynamic setting cannot be conducted in the large due to computational limitations, but with up to 460 candidates, a chain cap of 4 was best (in fact, better than 5).