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：我们提出了一种新型难民安置模型，该模型同时尊重接纳社区与难民自身的偏好。具体而言，给定代表当地社区的拓扑结构、占据部分拓扑顶点的居民集合，以及需安置在图结构空余顶点上的难民集合。居民与难民均对各自邻域结构存在偏好。本研究的核心问题在于寻找满足所有个体偏好的安置方案——用博弈论术语表述，即寻求满足特定稳定性定义的稳定解。我们考察了保证均衡存在性的条件，并研究了寻找此类稳定解的计算复杂度。鉴于该问题即使在极简设定下仍属NP难问题，我们采用参数化复杂度框架，从自然参数与给定拓扑结构约束两个维度对问题复杂度进行更精细化的分析。