We propose a novel model for refugee housing respecting the preferences of accepting community and refugees themselves. In particular, we are given a topology representing the local community, a set of inhabitants occupying some vertices of the topology, and a set of refugees that should be housed on the empty vertices of graph. Both the inhabitants and the refugees have preferences over the structure of their neighbourhood. We are specifically interested in the problem of finding housings such that the preferences of every individual are met; using game-theoretical words, we are looking for housings that are stable with respect to some well-defined notion of stability. We investigate conditions under which the existence of equilibria is guaranteed and study the computational complexity of finding such a stable outcome. As the problem is NP-hard even in very simple settings, we employ the parameterised complexity framework to give a finer-grained view on the problem's complexity with respect to natural parameters and structural restrictions of the given topology.

翻译：针对收容社区与难民自身偏好的尊重，我们提出了一种新颖的难民安置模型。具体而言，给定一个表征当地社区的拓扑结构、占据该拓扑部分顶点的居民集合，以及需安置在图中空余顶点上的难民集合。居民与难民均对自身邻域结构存在偏好。本研究特别关注如何找到满足每位个体偏好的安置方案；从博弈论角度而言，我们寻求的是在某种明确定义的稳定性概念下具有稳定性的安置方案。我们探究了保证均衡存在的条件，并研究了寻找此类稳定结果的计算复杂性。由于该问题即使在极简设定下仍具有NP难度，我们采用参数化复杂度框架，从自然参数和给定拓扑结构约束的角度，对该问题的复杂度进行了更精细的视角分析。