Budgeted Profit Maximization Under the Multiple Products Independent Cascade Model

Influence maximization problem asks for a small subset of nodes in a social network that could maximize the spread of influence, which finds important applications in viral marketing. Most existing works focus on maximizing the influence of a single product or products that are in pure competition. However, a company usually produces different products to meet the needs of different people in reality. In this paper, we focus on the propagation of multiple products and propose multiple products independent cascade (MPIC) model, which allows each user to adopt multiple products. Aiming to maximize the overall profit across all products, we study the budgeted profit maximization (BPM) problem. To give a high-quality solution for BPM problem under the MPIC model, we present a modified greedy algorithm and derive the performance guarantee in doing so. Furthermore, we show that the two-phase profit maximization algorithm can not only handle the large-scale networks but also give the same approximation ratio as the modified greedy. In addition, we propose the cost performance update heuristics algorithm that has the results close to the above algorithms, and the running time is less than one ten-thousandth of the greedy. Our experiments on three real datasets verify the correctness and effectiveness of our methods, as well as the advantage of our methods against the traditional methods.