We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of $\frac{e}{e-1}$, and provide a $\frac{4e}{e-1}$-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.

翻译：我们首次研究了在平均价值约束下，面向福利最大化的商品分配问题的集中式算法。我们证明，该问题在超越 $\frac{e}{e-1}$ 因子的近似上是 NP 难的，并提供了一个 $\frac{4e}{e-1}$ 近似的离线算法。针对在线场景，我们证明了在对抗性到达序列下无法实现任何非平凡的近似。在独立同分布到达序列下，我们提出了一种多项式时间在线算法，该算法能对最优（计算无限制）在线算法实现常数倍近似。与之相对，我们证明了在线算法无法对事后最优解实现常数倍近似。