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