Kidney Exchange: Faster Parameterized Algorithms and Tighter Lower Bounds

📝 Original Info

• Title: Kidney Exchange: Faster Parameterized Algorithms and Tighter Lower Bounds
• ArXiv ID: 2512.24037
• Date: 2025-12-30
• Authors: Aritra Banik, Sujoy Bhore, Palash Dey, Abhishek Sahu

📝 Abstract

The kidney exchange mechanism allows many patient-donor pairs who are otherwise incompatible with each other to come together and exchange kidneys along a cycle. However, due to infrastructure and legal constraints, kidney exchange can only be performed in small cycles in practice. In reality, there are also some altruistic donors who do not have any paired patients. This allows us to also perform kidney exchange along paths that start from some altruistic donor. Unfortunately, the computational task is NP-complete. To overcome this computational barrier, an important line of research focuses on designing faster algorithms, both exact and using the framework of parameterized complexity. The standard parameter for the kidney exchange problem is the number t of patients that receive a healthy kidney. The current fastest known deterministic FPT algorithm for this problem, parameterized by t, is O ⋆ (14 t ). In this work, we improve this by presenting a deterministic FPT algorithm that runs in time O ⋆ ((4e) t ) ≈ O ⋆ (10.88 t ). This problem is also known to be W[1]-hard parameterized by the treewidth of the underlying undirected graph. A natural question here is whether the kidney exchange problem admits an FPT algorithm paramet...

📄 Full Content

...(본문 내용이 길어 생략되었습니다. 사이트에서 전문을 확인해 주세요.)