We study a fair division model where indivisible items arrive sequentially, and must be allocated immediately and irrevocably. Previous work on online fair division has shown impossibility results in achieving approximate envy-freeness under these constraints. In contrast, we consider an informed setting where the algorithm has complete knowledge of future items, and aim to ensure that the cumulative allocation at each round satisfies approximate envy-freeness -- which we define as temporal envy-freeness up to one item (TEF1). We focus on settings where items can be exclusively goods or exclusively chores. For goods, while TEF1 allocations may not always exist, we identify several special cases where they do -- two agents, two item types, generalized binary valuations, unimodal preferences -- and provide polynomial-time algorithms for these cases. We also prove that determining the existence of a TEF1 allocation is NP-hard. For chores, we establish analogous results for the special cases, but present a slightly weaker intractability result. We also establish the incompatibility between TEF1 and Pareto-optimality, with the implication that it is intractable to find a TEF1 allocation that maximizes any $p$-mean welfare, even for two agents.

翻译：我们研究一种公平分配模型，其中不可分割的物品按序到达，且必须立即且不可撤销地进行分配。先前关于在线公平分配的研究已表明，在这些约束条件下实现近似无嫉妒性是不可能的。相比之下，我们考虑一种信息完备的设置，即算法完全知晓未来的物品，并旨在确保每一轮的累积分配满足近似无嫉妒性——我们将其定义为至多一件物品的时序无嫉妒性（TEF1）。我们重点关注物品仅为商品或仅为杂务的场景。对于商品，虽然TEF1分配可能并不总是存在，但我们识别出几种存在TEF1分配的特殊情况——两个智能体、两种物品类型、广义二元估值、单峰偏好——并为这些情况提供了多项式时间算法。我们还证明了判定TEF1分配是否存在是NP难的。对于杂务，我们在这些特殊情况下建立了类似的结果，但给出了稍弱的难解性结论。我们还证明了TEF1与帕累托最优性之间的不相容性，其含义是：即使对于两个智能体，寻找一个能最大化任意$p$均值福利的TEF1分配也是难解的。