Revenue maximization in campaigns with a viral-driven presale and a conformity-driven sales phase

Abstract We study the Revenue Maximization (RM) problem in a two-phase marketing scenario consisting of a presale phase and an official sale phase. In the presale phase, users are influenced through social diffusion and are offered discounts. In the official phase, mass-media influence is modeled as a community-based stochastic process, incorporating conformity effects within communities. This scenario better reflects real-world marketing practices. However, the resulting RM problem is NP-hard and non-submodular, rendering traditional greedy approaches ineffective. To address this, we employ the sandwich approximation (SA) strategy to provide theoretical guarantees. Furthermore, we propose the Community-Based Greedy Algorithm (CBGA), which incorporates a general improvement strategy applicable to greedy selection methods based on Monte Carlo simulation or Reverse Influence Sampling. CBGA adopts a divide-and-conquer approach by performing greedy selection within each community, thereby improving the runtime efficiency. The integration of CBGA with the SA strategy yields a structure-dependent theoretical guarantee, with the approximation quality determined by the number of boundary nodes between communities. We further extend our model to more general settings. We experimentally validate that CBGA matches the performance of all baselines but runs faster on six real-world datasets.