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