We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great interest to the AI community due to their applicability to real-world problems. Following some impossibility results, we restrict attention to matroid feasibility constraints that capture natural scenarios, such as the allocation of shifts to medical doctors, and the allocation of conference papers to referees. We focus on the common fairness notion of envy-freeness up to one good (EF1). Previous algorithms for finding EF1 allocations are either restricted to agents with identical feasibility constraints, or allow free disposal of items. An open problem is the existence of EF1 complete allocations among heterogeneous agents, where the heterogeneity is both in the agents' feasibility constraints and in their valuations. In this work, we make progress on this problem by providing positive and negative results for different matroid and valuation types. Among other results, we devise polynomial-time algorithms for finding EF1 allocations in the following settings: (i) $n$ agents with heterogeneous partition matroids and heterogeneous binary valuations, (ii) 2 agents with heterogeneous partition matroids and heterogeneous additive valuations, and (iii) at most 3 agents with heterogeneous binary valuations and identical base-orderable matroid constraints.
翻译:我们研究的是在具有可行性限制的添加剂中公平分配不可分割货物的问题,在这些环境中,每种代理都局限于在一组特定的可行性捆包中捆绑。这种情景对于AI社区非常感兴趣,因为它们适用于现实世界的问题。在取得一些不可能的结果之后,我们只注意那些捕捉自然情景的机器人可行性限制,例如向医生分配轮班,以及向裁判分配会议文件。我们注重的是嫉妒无忌妒至一种好处的共同公平概念(EF1)。以前为寻找EF1分配而采用的算法要么局限于具有相同可行性限制的代理人,要么允许免费处置物品。一个公开的问题是,在各种代理人中,EF1完全分配,其异质性既存在于代理人的可行性限制中,也存在于其估价中。在这项工作中,我们通过为不同的类甲状腺和估值类型提供正负结果,从而在这一问题上取得进展。除其他结果外,我们设计了在以下环境中寻找EF1分配的多种时间算法:(一) 具有不同间隔类配方的代理,或者允许自由处置物品。一个公开的问题在于,EF1在各种代理人之间分配,即EF1完全分配方,在各种配方之间,同时进行混合价格估值,2级,在可进行货币和固定的基级评估时,以及固定的基级定值上,在3的基质的基级的基级评估,(一),在基级的基级和基级定的基级上,(二)和基级,(基级,(基级,(一)和基级,(基级)进行。