Equilibrium of individual concern-critical influence maximization in virtual and real blending network

Recently, the Metaverse has received much attention, especially from large companies, such as Meta. The social nature of the Metaverse opens new ways for immersive social interactions that combine the strengths of physical and virtual worlds. This scenario creates new possibilities for social interactions that can worsen problems like the Echo chamber or the information cocoon effects. In this work, we devise a virtual and real blending network environment and introduce the concern vector indicator to explore the equilibrium of individual concern-critical influence maximization (EIC-cIM). We compute the complexity of the EIC-cIM and verify the modularity of the objective function. A surrogate objective function is introduced to tackle the problem of the EIC-cIM. We exploit the continuous relaxation technique to develop an approximate projected subgradient algorithm, which effectively guarantees the balance of individual concern in the information diffusion process. The experimental simulations on three network data sets demonstrate the effectiveness of our method, and the experimental results show that our proposed algorithm outperforms the existing heuristic algorithms by at least 23% in performance and even outperforms the max-greedy algorithm in some cases.