AI 中文总结
针对个性化双值估值下不可分物品与劳务的精确最大最小份额（MMS）分配这一开放问题，研究人员通过结合配额重新表述等方法，证明该分配始终存在且可在多项式时间内计算。
AI 中文摘要
最大最小份额（MMS）是不可分物品与劳务分配的核心公平基准。我们研究个性化双值设置下的加法估值，其中每个智能体对每件物品赋予两个智能体特定值中的一个。该设置下是否始终存在精确MMS分配仍是一个重大开放问题，Ebadian、Peters和Shah以及Garg、Huang和Segal-Halevi均强调了这一点。我们肯定地回答了该问题：我们证明对于物品和劳务，精确MMS分配始终存在，且可在多项式时间内计算。我们的证明结合了基于配额的重新表述、包络松弛、稀疏极点构造以及控制总舍入损失的基于流的舍入方法。
英文摘要
The maximin share (MMS) is a central fairness benchmark for allocating indivisible goods and chores. We study additive valuations in the personalized bivalued setting, where each agent assigns one of two agent-specific values to every item. Whether exact MMS allocations always exist in this setting has remained a major open question, as highlighted by Ebadian, Peters, and Shah and by Garg, Huang, and Segal-Halevi. We answer this question affirmatively: we prove that exact MMS allocations always exist for both goods and chores and can be computed in polynomial time. Our proof combines a quota-based reformulation with an envelope relaxation, a sparse extreme-point construction, and flow-based rounding that controls the total rounding loss.
