装箱与覆盖：推进最大最小份额公平性的研究前沿
Bin Packing and Covering: Pushing the Frontier on the Maximin Share Fairness
AI总结：
针对基于箱子数估值的公平分配问题中MMS准则难以完全满足的问题，提出基数与序数两类近似方案，为相关模型设计了常数近似算法，推进了MMS公平性研究。
摘要：
我们研究一个基础的公平分配问题，其中智能体的价值由用于打包或覆盖分配给它们的物品的箱子数量决定。公平性通过最大最小份额（MMS）准则评估。该问题不仅受实际应用驱动，也是研究群体公平性的天然框架。由于MMS并非总能满足，我们考虑两类近似：基数近似和序数近似。对于基数近似，我们放宽了箱子被打包或覆盖的要求；对于序数近似，我们放宽了被打包或覆盖的箱子数量。针对所有关注的模型，我们提出了常数近似算法。
英文摘要：
We study a fundamental fair allocation problem, where the agent's value is determined by the number of bins either used to pack or cover the items allocated to them. Fairness is evaluated using the maximin share (MMS) criterion. This problem is not only motivated by practical applications, but also serves as a natural framework for studying group fairness. As MMS is not always satisfiable, we consider two types of approximations: cardinal and ordinal. For cardinal approximation, we relax the requirements of being packed or covered for a bin, and for ordinal approximation, we relax the number of bins that are packed or covered. For all models of interest, we provide constant approximation algorithms.
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