Fair resource allocation is an important problem in many real-world scenarios, where resources such as goods and chores must be allocated among agents. In this survey, we delve into the intricacies of fair allocation, focusing specifically on the challenges associated with indivisible resources. We define fairness and efficiency within this context and thoroughly survey existential results, algorithms, and approximations that satisfy various fairness criteria, including envyfreeness, proportionality, MMS, and their relaxations. Additionally, we discuss algorithms that achieve fairness and efficiency, such as Pareto Optimality and Utilitarian Welfare. We also study the computational complexity of these algorithms, the likelihood of finding fair allocations, and the price of fairness for each fairness notion. We also cover mixed instances of indivisible and divisible items and investigate different valuation and allocation settings. By summarizing the state-of-the-art research, this survey provides valuable insights into fair resource allocation of indivisible goods and chores, highlighting computational complexities, fairness guarantees, and trade-offs between fairness and efficiency. It serves as a foundation for future advancements in this vital field.

翻译：公平资源分配是众多现实场景中的重要问题，其中商品与任务等资源需在智能体间分配。本综述深入探讨公平分配的复杂性，特别聚焦于不可分资源的相关挑战。我们在此背景下定义了公平性与效率性，系统梳理了满足各类公平准则（包括无嫉妒性、比例性、MMS及其松弛形式）的存在性结论、算法及近似方法。此外，我们探讨了兼顾公平与效率的算法（如帕累托最优与功利主义福利），并研究了这些算法的计算复杂度、公平分配的存在概率以及各公平概念下的公平代价。同时，我们涵盖不可分与可分物品的混合实例，并考察了不同的估值与分配场景。通过总结前沿研究，本综述为不可分商品与任务的公平资源分配提供了宝贵洞见，揭示了计算复杂性、公平性保障及公平与效率间的权衡，为该重要领域的未来发展奠定了基础。