Efficient hybrid rumor mitigation in dynamic and multilayer online social networks

The proliferation of malicious information, including fake news and rumors, within Online Social Networks (OSNs) has prompted considerable research into strategies that mitigate the adverse effects of such content. This study focuses on the problem of minimizing rumor influence in dynamic, multilayer OSNs. Given the rapid evolution of OSNs and their expanding functionalities, we introduce an innovative OSN representation as a dynamic multilayer network, incorporating heterogeneous propagation models across layers to effectively capture the complex structure of OSNs. To address the challenge, we propose a hybrid approach that integrates two strategies: the Node or Link Blocking Strategy (BNLS) and the Truth Campaign Strategy (TCS). This integration allows us to identify an optimal set of nodes for limiting rumor spread through a probabilistic framework grounded in network inference. We introduce a hybrid approach that combines BNLS and TCS for Rumor Influence Minimization, seeking to identify two optimal node sets, K+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K<^>+$$\end{document} and K-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K<^>-$$\end{document}, to limit rumor spread and support truth campaigns, respectively. This selection is made under the constraint |K+|+|K-|<= K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|K<^>+| + |K<^>-| \le K$$\end{document}, where K is a predefined budget. By leveraging the strengths of both strategies, our approach minimizes rumor influence effectively. Our method presents several advantages: it captures (1) the dynamic and multilayered representation of OSNs, (2) the evolving structural properties of networks, and (3) the temporal aspects of rumor propagation. To implement this solution, we develop the Hybrid Greedy Algorithm (HGA), which provides a (1-1/e)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1-1/\textit{e})$$\end{document}-approximation guarantee. Systematic experiments on both synthetic and real-world datasets across single and multilayer networks demonstrate the superior performance of our approach. The results indicate that our hybrid strategy outperforms recent state-of-the-art methods, validating its effectiveness for rumor influence minimization.