We propose a novel model for refugee housing respecting the preferences of the 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 the graph. Both the inhabitants and the refugees have preferences over the structure of their neighborhood. We are specifically interested in the problem of finding housing such that the preferences of every individual are met; using game-theoretical words, we are looking for housing that is 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 parameterized complexity framework to give a finer-grained view of the problem's complexity with respect to natural parameters and structural restrictions of the given topology.

翻译：我们提出了一种新颖的难民住房模型，该模型同时尊重接纳社区与难民自身的偏好。具体而言，我们给定一个表示当地社区结构的拓扑图，其中部分顶点已被原住居民占据，而难民则需被安置在图中空置的顶点上。原住居民与难民均对其邻里结构存在特定偏好。我们重点关注如何找到满足每个个体偏好的住房方案；用博弈论的术语来说，即寻求在某种明确定义的稳定性概念下达到稳定状态的住房配置。我们研究了保证均衡解存在的条件，并分析了寻找此类稳定结果的计算复杂度。由于即使在极简设定下该问题也属于NP难问题，我们采用参数化复杂度框架，针对自然参数与给定拓扑的结构限制，对问题复杂度进行更精细的刻画。