A Sampling-Free Anticipatory Algorithm for the Kidney Exchange Problem

Kidney exchange programs try to improve accessibility to kidney transplants by allowing incompatible patient-donor pairs to swap donors. Running such a program requires to solve an optimization problem (the Kidney Exchange Problem, or KEP) as new pairs arrive or, unfortunately, drop-off. The KEP is a stochastic online problem, and can greatly benefit from the use of anticipatory algorithms. Unfortunately, most such algorithms suffer from scalability issues due to the reliance on scenario sampling, limiting their practical applicability. Here, we recognize that the KEP allows for a sampling-free probabilistic model of future arrivals and drop-offs, which we capture via a so-called Abstract Exchange Graph (AEG). We show how an AEG-based approach can outperform sampling-based algorithms in terms of quality, while being comparable to a myopic algorithm in terms of scalability. While our current experimentation is preliminary and limited in scale, these qualities make our technique one of the few that can hope to address nation-wide programs with thousands of enrolled pairs.