MHPD: An efficient evaluation method for influence maximization on hypergraphs

Influence maximization problem (IM) has been extensively applied in fields such as viral marketing, rumor control, and infectious disease prevention. However, research on the IM problem has primarily focused on ordinary networks, with limited attention devoted to hypergraphs. Firstly, we propose an efficient evaluation method, i.e., the multiple-hop probability dissemination method (MHPD), aiming to accurately and rapidly evaluate the propagation capacity of selected nodes. The MHPD method is a universal approach that is applicable to various network types, including hypergraphs, and it accommodates multiple probabilistic spreading models. Then, based on MHPD, we propose two novel algorithms for solving IM problem, i.e., MHPD-greedy and MHPD-heuristic. MHPD-greedy employs MHPD to evaluate the marginal benefits of nodes and iteratively adds nodes with the maximum marginal benefit to the seed set. MHPD-heuristic utilizes MHPD to evaluate the propagation capacity of each node and select the top-$K$ nodes as the seeds. Experimental results on eight real-world hypergraphs and eight synthetic hypergraphs demonstrate that MHPD is capable of achieving near-identical accuracy in evaluating the propagation capability of both individual nodes and seed sets, while only incurring an average time overhead of merely 0.25 % compared to Monte Carlo method. In comparison with seven cutting-edge algorithms, MHPD-heuristic demonstrates superior solution accuracy. Notably, MHPD-greedy maintains 98.81 % of the solution accuracy while requiring only 0.11 % of the time cost compared to the Greedy method. Furthermore, MHPD-greedy achieves an average performance improvement of 23.4 % over the best baseline algorithm.