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.

翻译：本文提出了一种新的影响力传播模型，即互补竞争独立级联（C$^2$IC）模型。C$^2$IC模型统一了三种经典影响力模型：影响力增强（IB）模型、竞选无关独立级联（COIC）模型和带负面意见的独立级联（IC-N）模型。这是首个在多智能体环境下全面考虑互补与竞争影响力传播的模型。相应地，我们提出了互补竞争影响力最大化（C$^2$IM）问题。给定一个盟友种子集和一个对手种子集，C$^2$IM问题的目标是选择一组辅助节点，使其能够同时增强盟友传播并抑制对手传播。我们证明该问题是NP难的，且可推广影响力增强问题与影响力阻断问题。通过将不同级联优先级按单调性与子模性（M&S）成立条件分为4种情形，我们分别设计了4种算法，并给出了理论近似比。我们在真实社交网络上进行了大量实验，实验结果证明了所提算法的有效性。我们希望这项工作能激发未来更多关于构建更通用影响力模型的研究，从而为该领域的工作提供系统性支持。