Hyper-aware adaptive heuristic algorithms: A novel approach for seed selection in hypergraph-based diffusion

Influence maximization (IM) is a fundamental problem with broad applications in domains, such as social networks, information diffusion, and epidemic control. Traditional approaches predominantly model networks as ordinary graphs, which are limited in capturing complex higher-order group interactions. In contrast, hypergraphs provide a more natural and expressive representation of multi-node interactions. In this study, we investigate the IM problem on hypergraphs under the Susceptible-Infected spreading model with Contact Process dynamics. Leveraging node degree and hyperdegree, we propose four hyper-aware adaptive heuristic algorithms with distinct iterative update rules and systematically analyze the effects of incorporating the influence of selected seed nodes in first- and second-order neighbors on diffusion performance and computational efficiency. Extensive experiments on real-world and synthetic hypergraphs with varying degree heterogeneity demonstrate that the proposed algorithms consistently outperform baseline methods in terms of diffusion effectiveness, particularly under limited seed budgets, and exhibit strong robustness to variations in the hypergraph structure. Detailed analysis further reveals that the hyperdegree-scaled 1st-order neighbor reduction algorithm, which accounts for the influence of selected seeds in first-order neighbors, achieves an optimal trade-off between diffusion performance and computational efficiency, improving maximum effectiveness by 30.29% relative to baselines and reaching up to 63.42% improvement under constrained seed budgets.