The Parameterized Complexity of Welfare Guarantees in Schelling Segregation (Extended Abstract)

Argyrios Deligkas, Eduard Eiben, Tiger-Lily Goldsmith

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Schelling's model considers k types of agents each of whom needs to select a vertex on an undirected graph, where every agent prefers to 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 (WO) and Pareto optimality (PO), alongside the recently proposed notions of group-welfare optimality (GWO) and utility-vector optimality (UVO), both of which lie between WO and PO. Firstly, we focus on the fundamental case where k=2 and there are r red agents and b blue agents. We show that all solution-notions we consider are NP-hard to compute even when b=1 and that they are W[1]-hard when parameterized by r and b. In addition, we show that WO and GWO are NP-hard even on cubic graphs. We complement these negative results by an FPT algorithm parameterized by r, b and the maximum degree of the graph. For the general case with k types of agents, we prove that for any of the notions we consider the problem is W[1]-hard when parameterized by k for a large family of graphs that includes trees. We accompany these negative results with an XP algorithm parameterized by k and the treewidth of the graph.
Original languageEnglish
Title of host publicationThe 22nd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2023
Publication statusAccepted/In press - 4 Jan 2023
EventThe 22nd International Conference on Autonomous Agents and Multiagent Systems - London, United Kingdom
Duration: 29 May 20232 Jun 2023


ConferenceThe 22nd International Conference on Autonomous Agents and Multiagent Systems
Abbreviated titleAAMAS 2023
Country/TerritoryUnited Kingdom
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