aiqbench analysis
This research tackles the practical challenge of algorithm selection for the Maximum Clique Problem by introducing a dual-channel Graph Neural Network architecture. By jointly modeling local topological patterns via Graph Attention Networks and global statistical features with MLPs, the system achieves 90.43% accuracy in predicting optimal solvers across diverse graph instances. The work highlights the efficacy of integrating learned representations with conventional descriptors to automate solver choice in combinatorial optimization.
Instance-Aware Algorithm Selection for Maximum Clique via a Dual-Channel Graph Neural Architecture
arXiv:2508.08005v5 Announce Type: replace-cross Abstract: Although the Maximum Clique Problem (MCP) has been extensively studied and features a rich ecosystem of exact solvers, empirical evidence shows that solver performance varies substantially across graph families. Consequently, selecting an appropriate algorithm for a given instance remains an open and practically important challenge that has received little systematic attention. We address this gap by developing an instance-aware selection framework that systematically combines global statistical descriptors with learned topological representations. We construct a comprehensive benchmark by evaluating four state-of-the-art exact solvers on a diverse collection of graph instances and deriving both global statistical and local structural features. An evaluation of conventional classifiers establishes Random Forest as a strong baseline and reveals that connectivity and topological features are key predictors of performance. Motivated by these observations, we introduce a dual-channel architecture that jointly leverages a Graph Attention Network for capturing local neighborhood patterns and a Multilayer Perceptron for modeling global statistical features. Extensive experiments show that the proposed dual-channel model consistently surpasses classical baselines and the single-best solver, achieving 90.43% test accuracy. These findings demonstrate the value of integrating local topological encoding with global statistical cues for combinatorial algorithm selection. Code and models are available at: https://anonymous.4open.science/r/GAT-MLP-7E5F.
Abstract:Although the Maximum Clique Problem (MCP) has been extensively studied and features a rich ecosystem of exact solvers, empirical evidence shows that solver performance varies substantially across graph families. Consequently, selecting an appropriate algorithm for a given instance remains an open and practically important challenge that has received little systematic attention. We address this gap by developing an instance-aware selection framework that systematically combines global statistical descriptors with learned topological representations. We construct a comprehensive benchmark by evaluating four state-of-the-art exact solvers on a diverse collection of graph instances and deriving both global statistical and local structural features. An evaluation of conventional classifiers establishes Random Forest as a strong baseline and reveals that connectivity and topological features are key predictors of performance. Motivated by these observations, we introduce a dual-channel architecture that jointly leverages a Graph Attention Network for capturing local neighborhood patterns and a Multilayer Perceptron for modeling global statistical features. Extensive experiments show that the proposed dual-channel model consistently surpasses classical baselines and the single-best solver, achieving 90.43% test accuracy. These findings demonstrate the value of integrating local topological encoding with global statistical cues for combinatorial algorithm selection. Code and models are available at: this https URL.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2508.08005 [cs.LG]
(or arXiv:2508.08005v5 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2508.08005 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 294 words
