I. Introduction
In living kidney donation, a patient tries to find a friend or relative who is willing to donate one of her kidneys to the patient. Even if a patient finds such a living donor, this donor is often not medically compatible with the patient. Kidney exchange tries to solve this problem by finding constellations in which multiple such incompatible patient-donor pairs can exchange their kidney donors among each other. These exchanges are usually carried out in exchange cycles where the donor of a patient-donor pair always donates to the patient of the succeeding pair in the cycle and the patient of a pair receives a kidney donation from the donor of the preceding pair. In practice, the maximum size of these exchange cycles is commonly restricted to two or three due to the amount of medical resources that are required to carry out a transplant [2].