Influence Maximization with Spontaneous User Adoption

We incorporate the realistic scenario of spontaneous user adoption into influence propagation (also refer to as self-activation) and propose the self-activation independent cascade (SAIC) model: nodes may be self activated besides being selected as seeds, and influence propagates from both selected seeds and self activated nodes. Self activation occurs in many real world situations; for example, people naturally share product recommendations with their friends, even without marketing intervention. Under the SAIC model, we study three influence maximization problems: (a) boosted influence maximization (BIM) aims to maximize the total influence spread from both self-activated nodes and k selected seeds; (b) preemptive influence maximization (PIM) aims to find k nodes that, if self-activated, can reach the most number of nodes before other self-activated nodes; and (c) boosted preemptive influence maximization (BPIM) aims to select k seed that are guaranteed to be activated and can reach the most number of nodes before other self-activated nodes. We propose scalable algorithms for all three problems and prove that they achieve $1-1/e-\varepsilon$ approximation for BIM and BPIM and $1-\varepsilon$ for PIM, for any $\varepsilon > 0$. Through extensive tests on real-world graphs, we demonstrate that our algorithms outperform the baseline algorithms significantly for the PIM problem in solution quality, and also outperform the baselines for BIM and BPIM when self-activation behaviors are nonuniform across nodes.