AAMAS Conference 2025 Conference Paper
Neighborhood Stability in Assignments on Graphs
- Haris Aziz
- Grzegorz Lisowski
- Mashbat Suzuki
- Jeremy Vollen
We study the problem of assigning agents to the vertices of a graph such that no pair of neighbors can benefit from swapping assignments – a property we term neighborhood stability. We assume that agents’ utilities are based only on their preferences over the assignees of adjacent vertices and that those preferences are binary. Having shown that even this very restricted setting does not guarantee neighborhood stable assignments, we focus on special cases providing such guarantees. We show that when the graph is a cycle or a path, a neighborhood stable assignment always exists for any preference profile. Also, we give a general condition under which neighborhood stable assignments always exist. For each of these results, we give a polynomial-time algorithm to compute a neighborhood stable assignment.