关于圈与团的可达性
On Reachable Assignments in Cycles and Cliques
摘要：
在代理之间有效和公平地分配不可分割的资源是\emph{Multi-Agent-Systems}领域的一个共同问题。我们考虑这个问题的一个基于图的版本，称为可达性问题，由Gourves，Lesca和Wilczynski [AAAI，2017]引入。这个问题的输入包括一组代理，一组对象，代理的偏好对象，一个图形与代理作为顶点和边缘编码的代理可以相互交易资源，以及初始和目标分布的对象，其中每个代理拥有每个分布中的一个对象。问题是，通过一系列理性交易，目标分布是否可以达到。当两个参与者在图中是邻居，并且都获得了他们更喜欢的对象，而不是他们以前持有的对象时，交易是理性的。我们证明了可达图是NP难的，即使限制输入图是一个集团和开发的情况下，输入图是一个循环与$n$顶点的$O(n^3)$时间算法。
英文摘要：
The efficient and fair distribution of indivisible resources among agents is a common problem in the field of \emph{Multi-Agent-Systems}. We consider a graph-based version of this problem called Reachable Assignments, introduced by Gourves, Lesca, and Wilczynski [AAAI, 2017]. The input for this problem consists of a set of agents, a set of objects, the agent's preferences over the objects, a graph with the agents as vertices and edges encoding which agents can trade resources with each other, and an initial and a target distribution of the objects, where each agent owns exactly one object in each distribution. The question is then whether the target distribution is reachable via a sequence of rational trades. A trade is rational when the two participating agents are neighbors in the graph and both obtain an object they prefer over the object they previously held. We show that Reachable Assignments is NP-hard even when restricting the input graph to be a clique and develop an $O(n^3)$-time algorithm for the case where the input graph is a cycle with $n$ vertices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
