Distributionally Robust Cycle and Chain Packing With Application To Organ Exchange.

We consider the cycle packing problems motivated by kidney exchange. In kidney exchange, patients with willing but incompatible donors enter into an organized market and trade donors in cyclic structures. Exchange programs attempt to match patients and donors utilizing the quality of matches. Current methods use a point estimate for the utility of a potential match that is drawn from an unknown distribution over possible true qualities. We apply the conditional value-at-risk paradigm to the size-constrained cycle and chain packing problem. We derive sample average approximation and distributionally-robust-optimization approaches to maximize the true quality of matched organs in the face of uncertainty over the quality of potential matches. We test our approach on the realistic kidney exchange data and show they outperform the state-of-the-art approaches. In the experiments, we use randomly generated exchange graphs resembling the structure of real exchanges, using anonymized data from the United Network for Organ Sharing.