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.

翻译：联盟结构生成（CSG）是一个NP困难问题，旨在将智能体划分为互斥的群组以实现社会福利最大化。本文提出QuACS——一种面向诱导子图博弈（ISG）中联盟结构生成的新型混合量子经典算法。该算法从所有智能体同属单一联盟的初始结构出发，递归识别最优二划分子集。该问题被转化为二次无约束二元优化（QUBO）问题，并采用量子近似优化算法（QAOA）求解。对于$n$智能体ISG，我们证明所提算法在运行时间为$\mathcal{O}(n^2)$且期望近似比为$92\%$的条件下优于现有近似经典解法。此外，与现有量子方案相比，该算法所需的量子比特数显著降低，使得中等规模问题的实验成为可能。为验证QuACS的有效性，我们利用量子模拟在标准基准数据集上进行了实验。