New Seating Algorithm Lets Planners Design Stable Arrangements

Frederik Glitzner's new paper on arXiv tackles a classic multi-agent problem: seating agents with preferences over each other. Traditionally, the seating graph (e.g., a row of chairs or a round table) is fixed, making it difficult to guarantee stability or envy-freeness. Glitzner flips the script by treating the graph itself as a designable object for the central planner. This allows constructing seating arrangements that are pairwise-stable—meaning no two agents would prefer to swap seats with each other.

The framework assumes agents have ordinal preferences (rankings of others) and introduces a model similar to having spare seats. Glitzner shows that classical stable matching results can be adapted, providing efficient algorithms for approximately optimal designs. The paper also reveals tractability boundaries and surprising connections to computational problems like subgraph isomorphism, disjoint path partitioning, and bin-packing. For tech professionals, this means more practical tools for designing stable social or seating structures in conferences, offices, or team-based environments.