论文标题

EF2X分配协议,用于限制添加剂估值

An EF2X Allocation Protocol for Restricted Additive Valuations

论文作者

Akrami, Hannaneh, Rezvan, Rojin, Seddighin, Masoud

论文摘要

我们研究了将一组$ m $不可分割的商品分配给一组$ n $代理商的问题。嫉妒的柔和性达到任何商品(EFX)标准 - 要求没有代理在删除任何单一商品后更喜欢另一个代理商的束 - 当资源是一组不可分割的商品时,它是一种显着的嫉妒性。在本文中,我们研究了EFX概念的限制添加剂估值,即,每种商品都有一些非负值,每个代理只对某些商品感兴趣。 我们引入了一种名为EFKX的EFX自然放松,该放松要求在删除任何$ k $商品后,没有代理会羡慕其他代理商。我们的主要贡献是一种算法,该算法发现对限制的添加剂估值的完整(即没有好处)EF2X分配。在我们的算法中,我们设计了新概念,即可能具有独立利益的“配置”和“嫉妒 - 淘汰”。 我们还使用新工具来查找EFX分配,以限制添加估值,最多可丢弃$ \ lfloor n/2 \ rfloor -1 $商品。这将限制添加剂估值的最新技术提高了$ 2 $。

We study the problem of fairly allocating a set of $m$ indivisible goods to a set of $n$ agents. Envy-freeness up to any good (EFX) criteria -- which requires that no agent prefers the bundle of another agent after removal of any single good -- is known to be a remarkable analogous of envy-freeness when the resource is a set of indivisible goods. In this paper, we investigate EFX notion for the restricted additive valuations, that is, every good has some non-negative value, and every agent is interested in only some of the goods. We introduce a natural relaxation of EFX called EFkX which requires that no agent envies another agent after removal of any $k$ goods. Our main contribution is an algorithm that finds a complete (i.e., no good is discarded) EF2X allocation for the restricted additive valuations. In our algorithm we devise new concepts, namely "configuration" and "envy-elimination" that might be of independent interest. We also use our new tools to find an EFX allocation for restricted additive valuations that discards at most $\lfloor n/2 \rfloor -1$ goods. This improves the state of the art for the restricted additive valuations by a factor of $2$.

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