Solving the Kidney Exchange Problem Using Privacy-Preserving Integer Programming

The kidney exchange problem (KEP) seeks to determine a constellation of exchanges that maximizes the number of possible transplants between a set of patients and their incompatible donors. Recently, Secure Multi-Party Computation (SMPC) techniques were used to devise privacy-preserving protocols that allow the solving of the KEP in a distributed fashion. However, these protocols lack sufficient performance in practice. In the non-privacy-preserving case, the most efficient algorithms solving the KEP are based on integer programming. It is in this context, that we propose a privacy-preserving protocol based on these integer programming techniques that efficiently solves the KEP in a privacy-preserving fashion. We prove the security of this protocol and analyze its complexity. Furthermore, we provide a comprehensive performance evaluation of an implementation of the protocol in the SMPC benchmarking framework MP-SPDZ.