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The spread of rumors in online networks threatens public safety and resultsin economic losses. To overcome this problem, a lot of work studies the problemof rumor control which aims at limiting the spread of rumors. However, allprevious work ignores the relationship between the influence block effect andcounts of impressions on the user. In this paper, we study the problem ofminimizing the spread of rumors when impression counts. Given a graph $G(V,E)$,a rumor set $R \in V$ and a budget $k$, it aims to find a protector set $P \inV \backslash R$ to minimize the spread of the rumor set $R$ under the budget$k$. Due to the impression counts, two following challenges of our problem needto be overcome: (1) our problem is NP-hard; (2) the influence block isnon-submodular, which means a straightforward greedy approach is notapplicable. Hence, we devise a branch-and-bound framework for this problem witha ($1-1/e-\epsilon$) approximation ratio. To further improve the efficiency, wespeed up our framework with a progressive upper bound estimation method, whichachieves a ($1-1/e-\epsilon - \rho$) approximation ratio. We conductexperiments on real-world datasets to verify the efficiency, effectiveness, andscalability of our methods.

Proactive Rumor Control: When Impression Counts (Full Version)