Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-09-10 , DOI: 10.1016/j.tcs.2020.08.030
Qiufen Ni; Jianxiong Guo; Chuanhe Huang; Weili Wu

Social networks provide us a convenient platform to communicate and share information or ideas with each other, but it also causes many negative effects at the same time, such as, the spread of misinformation or rumor in social networks may cause public panic and even serious economic or political crisis. In this paper, we propose a Community-based Rumor Blocking Problem (CRBMP), i.e., selecting a set of seed users from all communities as protectors with the constraint of budget b such that the expected number of users eventually not being influenced by rumor sources is maximized. We consider the community structure in social networks and solve our problem in two stages, in the first stage, we allocate budget b for all the communities, this sub-problem whose objective function is proved to be monotone and DR-submodular, so we can use the method of submodular function maximization on an integer lattice, which is different from most of the existing work with the submodular function over a set function. Then a greedy community budget allocation algorithm is devised to get an $1-1/e$ approximation ratio; we also propose a speed-up greedy algorithm which greatly reduces the time complexity for the community budget allocation and can get an $1-1/e-ϵ$ approximation guarantee meanwhile. Next we solve the Protector Seed Selection (PSS) problem in the second stage after we obtained the budget allocation vector for communities, we greedily choose protectors for each community with the budget constraints to achieve the maximization of the influence of protectors. The greedy algorithm for PSS problem can achieve a 1/2 approximation guarantee. We also consider a special case where the rumor just originates from one community and does not spread out of its own community before the protectors are selected, the proposed algorithm can reduce the computational cost than the general greedy algorithm since we remove the uninfected communities. Finally, we conduct extensive experiments on three real world data sets, the results demonstrate the effectiveness of the proposed algorithm and its superiority over other methods.

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