GCS-Q: Quantum Graph Coalition Structure Generation

The problem of generating an optimal coalition structure for a given game rational agents is to find partition that maximizes their social welfare and known be NP-hard. Though there are algorithmic solutions with high computational complexity available this combinatorial optimization problem, it unknown whether quantum-supported may outperform classical algorithms. In paper, we propose novel solution generation in Induced Subgraph Games (ISGs). Our hybrid classical-quantum algorithm, called GCS-Q, iteratively splits n-agent graph into two nonempty subsets order obtain higher value. GCS-Q solves the split $$\mathcal {O}(n)$$ times, exploring {O}(2^n)$$ partitions at each step. particular, reformulated as QUBO executed on quantum annealer, which capable providing linear time respect n. We show outperforms currently best solvers ISGs its runtime $$n^2$$ expected approximation ratio $$93\%$$ standard benchmark datasets.