On coalition formation with sparse synergies

We consider coalition formation problems for agents with an underlying synergistic graph, where edges between agents represent some vital synergistic link, such as communication, trust, or physical constraints. A coalition is infeasible if its members do not form a connected subgraph, meaning parts of the coalition are isolated from others. Current state-of-the-art coalition formation algorithms are not designed for problems over synergistic graphs. They assume that all coalitions are feasible and so involve redundant computation when this is not the case. Accordingly, we propose algorithms, namely D-SlyCE and DyCE, to enumerate all feasible coalitions in a distributed fashion and find the optimal feasible coalition structure respectively. When evaluated on a variety of synergistic graphs, D-SlyCE is up to 660 times faster while DyCE is up to 7 x 10⁴ times faster than the state-of-the-art algorithms. For particular classes of graphs, D-SlyCE is the first to enumerate valid coalition values for up to 50 agents and DyCE is the first algorithm to find the optimal coalition structure for up to 30 agents in minutes as opposed to months for previous algorithms.