Jointly Complementary&Competitive Influence Maximization with Concurrent Ally-Boosting and Rival-Preventing

In this paper, we propose a new influence spread model, namely, Complementary\&Competitive Independent Cascade (C$^2$IC) model. C$^2$IC model generalizes three well known influence model, i.e., influence boosting (IB) model, campaign oblivious (CO)IC model and the IC-N (IC model with negative opinions) model. This is the first model that considers both complementary and competitive influence spread comprehensively under multi-agent environment. Correspondingly, we propose the Complementary\&Competitive influence maximization (C$^2$IM) problem. Given an ally seed set and a rival seed set, the C$^2$IM problem aims to select a set of assistant nodes that can boost the ally spread and prevent the rival spread concurrently. We show the problem is NP-hard and can generalize the influence boosting problem and the influence blocking problem. With classifying the different cascade priorities into 4 cases by the monotonicity and submodularity (M\&S) holding conditions, we design 4 algorithms respectively, with theoretical approximation bounds provided. We conduct extensive experiments on real social networks and the experimental results demonstrate the effectiveness of the proposed algorithms. We hope this work can inspire abundant future exploration for constructing more generalized influence models that help streamline the works of this area.