We study the online fair division of indivisible items with additive utilities, where items arrive sequentially and must be irrevocably allocated upon arrival. Considering various fairness notions, we focus on designing online algorithms that produce fair or approximately fair allocations for any instance. We measure algorithm performance using the competitive ratio, defined as the worst-case ratio between the fairness guarantee achieved by the online algorithm and that of an optimal offline allocation with full knowledge of future arrivals. We examine a broad spectrum of models, including the allocation of goods or chores, normalized versus non-normalized utilities, and identical versus general utility functions. We address the majority of the unresolved cases by providing online algorithms or proving the limits of the competitive ratio achievable by online algorithms. In most cases, the algorithms are shown to be optimal.

翻译：我们研究了具有可加性效用的不可分割物品在线公平分配问题，其中物品按顺序到达且必须在到达时进行不可撤销的分配。考虑到各种公平性概念，我们专注于设计能够为任何实例产生公平或近似公平分配的在线算法。我们使用竞争比来衡量算法性能，该比例定义为在线算法实现的公平性保证与完全了解未来到达情况的最优离线分配所实现的公平性保证之间的最坏情况比率。我们考察了广泛的模型，包括物品或杂务的分配、归一化与非归一化效用、以及相同与一般效用函数。我们通过提供在线算法或证明在线算法可实现的竞争比极限，解决了大部分未解决的情况。在大多数情况下，这些算法被证明是最优的。