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：公平资源分配是许多现实场景中的重要问题，其中诸如商品和任务等资源需在多个智能体之间进行分配。本综述深入探讨了公平分配的复杂性，特别聚焦于不可分割资源带来的挑战。我们在此背景下定义了公平性与效率，并全面梳理了满足各种公平性准则（包括无嫉妒性、比例性、最大最小份额及其松弛形式）的存在性结论、算法及近似方法。此外，我们讨论了同时实现公平性与效率的算法，例如帕累托最优和功利主义社会福利。我们还研究了这些算法的计算复杂度、找到公平分配的可能性，以及每种公平性概念对应的公平代价。此外，本文涵盖了不可分割与可分割物品的混合场景，并探讨了不同的估值与分配设置。通过总结前沿研究，本综述为不可分割商品与任务的公平资源分配提供了宝贵见解，重点阐述了计算复杂性、公平性保证以及公平性与效率之间的权衡关系。这为该重要领域的未来发展奠定了基础。