QuACS: Variational Quantum Algorithm for Coalition Structure Generation in Induced Subgraph Games

Abstract

Coalition Structure Generation (CSG) is an NP-Hard problem in which agents are partitioned into mutually exclusive groups to maximize their social welfare. In this work, we propose QuACS, a novel hybrid quantum classical algorithm for Coalition Structure Generation in Induced Subgraph Games (ISGs). Starting from a coalition structure where all the agents belong to a single coalition, QuACS recursively identifies the optimal partition into two disjoint subsets. This problem is reformulated as a QUBO and then solved using QAOA. Given an $n$-agent ISG, we show that the proposed algorithm outperforms existing approximate classical solvers with a runtime of $\mathcal{O}(n^2)$ and an expected approximation ratio of $92\%$. Furthermore, it requires a significantly lower number of qubits and allows experiments on medium-sized problems compared to existing quantum solutions. To show the effectiveness of QuACS we perform experiments on standard benchmark datasets using quantum simulation.