Allocating resources to individuals in a fair manner has been a topic of interest since ancient times, with most of the early mathematical work on the problem focusing on resources that are infinitely divisible. Over the last decade, there has been a surge of papers studying computational questions regarding the indivisible case, for which exact fairness notions such as envy-freeness and proportionality are hard to satisfy. One main theme in the recent research agenda is to investigate the extent to which their relaxations, like maximin share fairness (MMS) and envy-freeness up to any good (EFX), can be achieved. In this survey, we present a comprehensive review of the recent progress made in the related literature by highlighting different ways to relax fairness notions, common algorithm design techniques, and the most interesting questions for future research.

翻译：自远古时代以来，以公平方式向个体分配资源便是一个备受关注的话题。早期的相关数学研究多聚焦于可无限分割的资源。在过去十年间，涌现了大量探讨不可分割物品计算问题的论文，在此类情境下，诸如无嫉妒性与比例性等精确公平概念难以实现。近期研究议程的主要主题之一，便是探究其松弛概念（如最大化份额公平性（MMS）和无嫉妒至任意物品（EFX））能在多大程度上得以实现。本综述通过强调松弛公平概念的不同方式、常用算法设计技术以及未来研究中最具趣味性的问题，对相关文献中的近期进展进行了全面回顾。