  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.
