发表机构
School of Computer Science and Technology, Shandong University; Department of Computing, The Hong Kong Polytechnic University（山东大学计算机科学与技术学院; 香港理工大学计算系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于 Simmons-Su 框架和 Sperner 引理，通过修改现有舍入技术，证明了离散杂务切割中存在连通的 EF1 分配。
AI 中文摘要
在本文中，我们证明了离散杂务中至多一件物品无嫉妒（EF1）分配的存在性。我们的方法建立在 Simmons-Su 的强大框架之上，该框架利用 Sperner 引理保证存在一个与一系列相似分数分配序列相对应的单纯形，确保每个代理对不同捆绑包感到满意。Bilò 等人 [2022] 引入了一种舍入技术，将分数分配转换为最多四个代理时商品的连通整数 EF1 分配，该方法后来由 Igarashi [2023] 扩展以适用于任意数量的代理。然而，这些针对商品的舍入技术不能直接应用于杂务，因为两种设置中 EF1 的定义不同。为克服这种不对称性，我们修改了现有的舍入技术，并证明了离散杂务中存在连通的 EF1 分配。
英文摘要
In this paper, we prove the existence of an envy-free up to one item (EF1) division for a discrete chore. Our approach builds on the powerful framework of Simmons-Su, which leverages Sperner's lemma to guarantee the existence of a simplex corresponding to a sequence of similar fractional divisions, ensuring that each agent is satisfied with a different bundle. Bilò et al. [2022] introduced a rounding technique that converts the fractional divisions into a connected integral EF1 division for goods when there are at most four agents, and this method was later extended by Igarashi [2023] to accommodate any number of agents. However, these rounding techniques for goods do not directly apply to chores because the definitions of EF1 differ in the two settings. To overcome this asymmetry, we modify the existing rounding techniques and show that connected EF1 divisions exist for a discrete chore.
CommentsFull version of the paper appeared in IJCAI-ECAI 2026
