发表机构
TU Clausthal; IIT Jodhpur（克劳斯塔尔工业大学; 焦特布尔印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对外部补贴不现实的问题，本研究提出仅允许代理间按个体预算支付以恢复无嫉妒分配，证明一般问题NP难但参数化可解，并给出高效算法。
AI 中文摘要
当不可分割商品的无嫉妒分配不存在时，货币转移可以恢复无嫉妒性。然而，现有关于补贴公平分配的研究通常假设这些支付由外部来源提供，这一假设在许多应用中可能不切实际。我们通过仅允许代理之间的货币转移来解决这一限制，每个代理的支付受其个体预算约束。我们证明，虽然确定给定分配在个体预算下能否通过支付实现无嫉妒是多项式时间可解的，但从零开始计算此类分配的一般问题即使代理拥有相对较大的预算也是NP困难的。受此难解性启发，我们进行了参数化复杂度分析，建立了关于商品数量或代理数量与商品类型联合参数的固定参数可解性，并在若干特殊情况下提供了高效算法。对于显式列出的物品，我们的基于类型的算法回答了T. T. Nguyen和J. Rothe的开放问题中关于无嫉妒的部分，该问题出自《不可分割物品公平分配的复杂度结果与精确算法：综述》。
英文摘要
When an envy-free allocation of indivisible goods does not exist, monetary transfers can restore envy-freeness. Existing work on fair division with subsidies, however, typically assumes that these payments are provided by an external source, an assumption that may be unrealistic in many applications. We address this limitation by allowing only monetary transfers between agents, with each agent's payments constrained by their individual budget. We show that while it is polynomial-time tractable to determine whether a given allocation can be made envy-free by payments under individual budgets, the general problem of computing such an allocation from scratch is NP-hard, even when agents have relatively large budgets. Motivated by this intractability, we conduct a parameterized complexity analysis, establishing fixed-parameter tractability with respect to the number of goods or to the joint parameter number of agents and good types, and we provide efficient algorithms in several special cases. For explicitly listed items, our type-based algorithm answers the envy-freeness part of an open question of T. T. Nguyen and J. Rothe, "Complexity Results and Exact Algorithms for Fair Division of Indivisible Items: A Survey."
