# Host Community Respecting Refugee Housing

## TL;DR

This paper introduces a new model for refugee housing that respects community and refugee preferences, analyzing the existence and computational complexity of stable housing arrangements within a graph-based community topology.

## Contribution

It formulates a game-theoretic model for refugee housing, investigates conditions for stable solutions, and analyzes the problem's NP-hardness and parameterized complexity.

## Key findings

- Existence of stable housing arrangements is guaranteed under certain conditions.
- The problem is NP-hard even in simple cases.
- Parameterized complexity provides insights into computational feasibility.

## 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.