Parameterized Algorithms for Optimal Refugee Resettlement

TL;DR

This paper explores the computational complexity of various formulations of the Optimal Refugee Resettlement problem, providing algorithms for some cases and hardness results for others, considering feasibility, preferences, and utilities.

Contribution

It introduces parameterized algorithms and complexity results for multiple variants of the refugee resettlement problem, including feasibility, Pareto-optimality, and utility maximization.

Findings

Fixed-parameter tractable algorithms for certain parameterizations.

Tight intractability results for other variants.

Comprehensive complexity analysis of the problem variants.

Abstract

We study variants of the Optimal Refugee Resettlement problem where a set $F$ of refugee families need to be allocated to a set $L$ of possible places of resettlement in a feasible and optimal way. Feasibility issues emerge from the assumption that each family requires certain services (such as accommodation, school seats, or medical assistance), while there is an upper and, possibly, a lower quota on the number of service units provided at a given place. Besides studying the problem of finding a feasible assignment, we also investigate two natural optimization variants. In the first one, we allow families to express preferences over $P$, and we aim for a Pareto-optimal assignment. In a more general setting, families can attribute utilities to each place in $P$, and the task is to find a feasible assignment with maximum total utilities. We study the computational complexity of all three variants in a multivariate fashion using the framework of parameterized complexity. We provide fixed-parameter tractable algorithms for a handful of natural parameterizations, and complement these tractable cases with tight intractability results.