The Parameterized Complexity of Welfare Guarantees in Schelling Segregation

Schelling's model considers 𝑘 types of agents each of whom needs to select a vertex on an undirected graph, where every agent prefers neighbor agents of the same type. We are motivated by a recent line of work that studies solutions that are optimal with respect to notions related to the welfare of the agents. We explore the parameterized complexity of computing such solutions. We focus on the well-studied notions of social welfare and Pareto optimality, alongside the recently proposed notions of group-welfare optimality and utility-vector optimality.