We study the fair allocation of indivisible items under relevance constraints, where each agent has a set of relevant items and can only receive items that are relevant to them. While the relevance constraint has been studied in recent years, existing work has largely focused on envy-freeness. Our work extends this study to other key fairness criteria -- such as proportionality, equitability, and their relaxations -- in settings where the items may be goods, chores, or a mixture of both. We complement the literature by presenting a picture of the existence and computational complexity of the considered criteria.

翻译：本文研究不可分割物品在相关性约束下的公平分配问题，其中每个智能体拥有一组相关物品，且只能获得与其相关的物品。尽管相关性约束近年来已得到研究，但现有工作主要聚焦于无嫉妒性。本研究将该问题拓展至其他关键公平性准则——例如比例性、均衡性及其松弛形式——并涵盖物品可能为物品、杂务或两者混合的情境。通过系统呈现所研究准则的存在性与计算复杂性图景，本文对现有文献形成了重要补充。