🤖 AI Summary
Refugee resettlement faces significant challenges in fostering social integration, particularly due to misalignment between host community acceptance and refugee housing preferences.
Method: This paper introduces a stable housing allocation model that jointly incorporates neighborhood structure preferences of both host residents and refugees. It formulates community acceptance and refugee preferences as a bidirectional stability problem on graphs, defines a novel notion of stable solution balancing fairness and feasibility, and establishes a theoretical framework for its existence and computational complexity.
Contributions: We prove that stable solutions do not always exist on general graphs and characterize sufficient conditions for existence. We identify polynomial-time solvable subclasses—parameterized by pathwidth and maximum degree—and design fixed-parameter tractable algorithms. Our work provides a computationally grounded theoretical foundation and algorithmic tools for designing integration-aware refugee housing policies.
📝 Abstract
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.
