Welfare Guarantees in Schelling Segregation

Schelling's model is an influential that reveals how individual perceptions and incentives can lead to residential segregation. Inspired by a recent stream of work, we study welfare guarantees complexity in this with respect several measures. First, show while maximizing the social NP-hard, computing assignment agents nodes any topology graph approximately half maximum be done polynomial time. We then consider Pareto optimality, introduce two new optimality notions based on it, establish mostly tight bounds worst-case loss for assignments satisfying these as well such assignments. In addition, tree topologies, it possible decide whether there exists gives every agent positive utility time; moreover, when node has degree at least $2$, always found efficiently.