A Thorough Comparison Between Independent Cascade and Susceptible-Infected-Recovered Models

Panfeng Liu, Guoliang Qiu, Biaoshuai Tao, Kuan Yang
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Abstract

We study cascades in social networks with the independent cascade (IC) model and the Susceptible-Infected-recovered (SIR) model. The well-studied IC model fails to capture the feature of node recovery, and the SIR model is a variant of the IC model with the node recovery feature. In the SIR model, by computing the probability that a node successfully infects another before its recovery and viewing this probability as the corresponding IC parameter, the SIR model becomes an "out-going-edge-correlated" version of the IC model: the events of the infections along different out-going edges of a node become dependent in the SIR model, whereas these events are independent in the IC model. In this paper, we thoroughly compare the two models and examine the effect of this extra dependency in the SIR model. By a carefully designed coupling argument, we show that the seeds in the IC model have a stronger influence spread than their counterparts in the SIR model, and sometimes it can be significantly stronger. Specifically, we prove that, given the same network, the same seed sets, and the parameters of the two models being set based on the above-mentioned equivalence, the expected number of infected nodes at the end of the cascade for the IC model is weakly larger than that for the SIR model, and there are instances where this dominance is significant. We also study the influence maximization problem with the SIR model. We show that the above-mentioned difference in the two models yields different seed-selection strategies, which motivates the design of influence maximization algorithms specifically for the SIR model. We design efficient approximation algorithms with theoretical guarantees by adapting the reverse-reachable-set-based algorithms, commonly used for the IC model, to the SIR model.
独立级联模型与易感-感染-恢复模型的全面比较
我们用独立级联(IC)模型和易感-感染-恢复(SIR)模型来研究社交网络中的级联。已被广泛研究的 IC 模型未能捕捉到节点恢复的特征,而 SIR 模型是 IC 模型的一个变体,具有节点恢复的特征。在 SIR 模型中,通过计算一个节点在恢复之前成功感染另一个节点的概率,并将该概率视为相应的 IC 参数,SIR 模型成为 IC 模型的 "出边相关 "版本:在 SIR 模型中,节点不同出边的感染事件变得相互依赖,而在 IC 模型中,这些事件是独立的。在本文中,我们全面比较了这两种模型,并研究了 SIR 模型中这种额外依赖性的影响。通过精心设计的耦合论证,我们证明了 IC 模型中的种子比 SIR 模型中的种子具有更强的影响力传播,有时甚至强得多。具体来说,我们证明了在相同的网络、相同的种子集以及根据上述等价性设置两个模型的参数的情况下,IC 模型在级联结束时受感染节点的预期数量弱于 SIR 模型,而且在某些情况下这种优势是显著的。我们还研究了 SIR 模型的影响最大化问题。我们发现,上述两种模型的差异会产生不同的种子选择策略,这促使我们设计出专门针对 SIR 模型的影响力最大化算法。我们通过将常用于 IC 模型的基于反向可达集的算法调整到 SIR 模型,设计出了具有理论保证的高效近似算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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