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GCS-Q: Quantum Graph Coalition Structure Generation

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Computational Science – ICCS 2023 (ICCS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14077))

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Abstract

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 known to be NP-hard. Though there are algorithmic solutions with high computational complexity available for this combinatorial optimization problem, it is unknown whether quantum-supported solutions may outperform classical algorithms.

In this paper, we propose a novel quantum-supported solution for coalition structure generation in Induced Subgraph Games (ISGs). Our hybrid classical-quantum algorithm, called GCS-Q, iteratively splits a given n-agent graph game into two nonempty subsets in order to obtain a coalition structure with a higher coalition value. The GCS-Q solves the optimal split problem \(\mathcal {O}(n)\) times, exploring \(\mathcal {O}(2^n)\) partitions at each step. In particular, the optimal split problem is reformulated as a QUBO and executed on a quantum annealer, which is capable of providing the solution in linear time with respect to n. We show that GCS-Q outperforms the currently best classical and quantum solvers for coalition structure generation in ISGs with its runtime in the order of \(n^2\) and an expected approximation ratio of \(93\%\) on standard benchmark datasets.

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Notes

  1. 1.

    Notice that to better fit standard graph games studied in the literature, we omit self-loop, which would require sampling other n values. However, the GCS-Q formulation is suitable for dealing with graphs containing self-loop.

  2. 2.

    A comparison between Advantage with the D-Wave 2000Q is reported [10].

  3. 3.

    https://docs.dwavesys.com/docs/latest/index.html.

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Acknowledgments

This work has been funded by the German Ministry for Education and Research (BMB+F) in the project QAI2-QAICO under grant 13N15586.

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Correspondence to Antonio Macaluso .

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Code Availability

All code to generate the data, figures, analyses and additional technical details on the experiments are available at https://github.com/supreethmv/GCS-Q.

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Venkatesh, S.M., Macaluso, A., Klusch, M. (2023). GCS-Q: Quantum Graph Coalition Structure Generation. In: Mikyška, J., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2023. ICCS 2023. Lecture Notes in Computer Science, vol 14077. Springer, Cham. https://doi.org/10.1007/978-3-031-36030-5_11

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  • DOI: https://doi.org/10.1007/978-3-031-36030-5_11

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