Designing dataless neural networks for kidney exchange variants

Kidney transplantation is vital for treating end-stage renal disease, impacting roughly one in a thousand Europeans. The search for a suitable deceased donor often leads to prolonged and uncertain wait times, making living donor transplants a viable alternative. However, approximately 40% of living donors are incompatible with their intended recipients. Therefore, many countries have established kidney exchange programs, allowing patients with incompatible donors to participate in “swap” arrangements, exchanging donors with other patients in similar situations. Several variants of the vertex-disjoint cycle cover problem model the above problem, which deals with different aspects of kidney exchange as required. This paper discusses several specific vertex-disjoint cycle cover variants and deals with finding the exact solution. We employ the dataless neural networks framework to establish single differentiable functions for each variant. Recent research highlights the framework’s effectiveness in representing several combinatorial optimization problems. Inspired by these findings, we propose customized dataless neural networks for vertex-disjoint cycle cover variants. We derive a differentiable function for each variant and prove that the function will attain its minimum value if an exact solution is found for the corresponding problem variant. We also provide proof of the correctness of our approach.