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Think Globally, Act Locally: On the Optimal Seeding for Nonsubmodular Influence Maximization
arXiv - CS - Discrete Mathematics Pub Date : 2020-03-23 , DOI: arxiv-2003.10393
Grant Schoenebeck, Biaoshuai Tao, Fang-Yi Yu

We study the $r$-complex contagion influence maximization problem. In the influence maximization problem, one chooses a fixed number of initial seeds in a social network to maximize the spread of their influence. In the $r$-complex contagion model, each uninfected vertex in the network becomes infected if it has at least $r$ infected neighbors. In this paper, we focus on a random graph model named the stochastic hierarchical blockmodel, which is a special case of the well-studied stochastic blockmodel. When the graph is not exceptionally sparse, in particular, when each edge appears with probability $\omega(n^{-(1+1/r)})$, under certain mild assumptions, we prove that the optimal seeding strategy is to put all the seeds in a single community. This matches the intuition that in a nonsubmodular cascade model placing seeds near each other creates synergy. However, it sharply contrasts with the intuition for submodular cascade models (e.g., the independent cascade model and the linear threshold model) in which nearby seeds tend to erode each others' effects. Our key technique is a novel time-asynchronized coupling of four cascade processes. Finally, we show that this observation yields a polynomial time dynamic programming algorithm which outputs optimal seeds if each edge appears with a probability either in $\omega(n^{-(1+1/r)})$ or in $o(n^{-2})$.

中文翻译:

放眼全球,局部行动:关于非次模块影响最大化的最佳种子

我们研究了 $r$-complex contagion 影响最大化问题。在影响力最大化问题中,人们在社交网络中选择固定数量的初始种子,以最大化其影响力的传播。在 $r$-复杂传染模型中,如果网络中每个未感染的顶点至少有 $r$ 被感染的邻居,它就会被感染。在本文中,我们关注一个名为随机分层块模型的随机图模型,它是经过充分研究的随机块模型的一个特例。当图不是特别稀疏时,特别是当每条边以 $\omega(n^{-(1+1/r)})$ 出现的概率时,在某些温和的假设下,我们证明了最优播种策略是将所有种子放在一个社区中。这与在非子模块级联模型中将种子彼此靠近放置会产生协同作用的直觉相匹配。然而,它与子模块级联模型(例如,独立级联模型和线性阈值模型)的直觉形成鲜明对比,其中附近的种子往往会削弱彼此的影响。我们的关键技术是四个级联过程的新型时间异步耦合。最后,我们表明这个观察产生了一个多项式时间动态规划算法,如果每条边出现的概率在 $\omega(n^{-(1+1/r)})$ 或 $o( n^{-2})$。我们的关键技术是四个级联过程的新型时间异步耦合。最后,我们表明这个观察产生了一个多项式时间动态规划算法,如果每条边出现的概率在 $\omega(n^{-(1+1/r)})$ 或 $o( n^{-2})$。我们的关键技术是四个级联过程的新型时间异步耦合。最后,我们表明这个观察产生了一个多项式时间动态规划算法,如果每条边出现的概率在 $\omega(n^{-(1+1/r)})$ 或 $o( n^{-2})$。
更新日期:2020-03-24
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