GCS-Q: Quantum Graph Coalition Structure Generation

The problem of generating an optimal coalition structure for a given coalition game of rational agents is to find a partition that maximizes their social welfare and is known to be NP-hard. This paper proposes GCS-Q, a novel quantum-supported solution for Induced Subgraph Games (ISGs) in coalition structure generation. GCS-Q starts by considering the grand coalition as initial coalition structure and proceeds by iteratively splitting the coalitions into two nonempty subsets to obtain a coalition structure with a higher coalition value. In particular, given an n-agent ISG, the GCS-Q solves the optimal split problem O (n) times using a quantum annealing device, exploring O(2n) partitions at each step. We show that GCS-Q outperforms the currently best classical solvers with its runtime in the order of n2 and an expected worst-case approximation ratio of 93% on standard benchmark datasets.