GCS-Q: Quantum Graph Coalition Structure Generation

TL;DR

GCS-Q introduces a quantum-supported method for coalition structure generation in Induced Subgraph Games, significantly improving runtime and approximation ratio over classical solvers.

Contribution

The paper presents GCS-Q, a novel quantum-based approach that efficiently explores coalition partitions, outperforming classical methods in speed and solution quality.

Findings

GCS-Q achieves runtime in the order of n^2.

GCS-Q attains an expected worst-case approximation ratio of 93%.

GCS-Q outperforms classical solvers on benchmark datasets.

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 is known to be NP-hard. This paper proposes GCS-Q, a novel quantum-supported solution for Induced Subgraph Games (ISGs) in coalition structure generation. GCS-Q starts by considering the grand coalition as initial coalition structure and proceeds by iteratively splitting the coalitions into two nonempty subsets to obtain a coalition structure with a higher coalition value. In particular, given an $n$-agent ISG, the GCS-Q solves the optimal split problem $\mathcal{O} (n)$ times using a quantum annealing device, exploring $\mathcal{O}(2^n)$ partitions at each step. We show that GCS-Q outperforms the currently best classical solvers with its runtime in the order of $n^2$ and an expected worst-case approximation ratio of $93\%$ on standard benchmark datasets.