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arXiv 1602.01003cs.SIcs.MAcs.SYeess.SYmath.OCphysics.soc-ph
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利用节点中心性与最优控制最大化社交网络中的信息扩散

Using Node Centrality and Optimal Control to Maximize Information Diffusion in Social Networks

Indian Institute of Science(印度科学学院)

Kundan Kandhway, Joy Kuri

AI总结:

本文研究如何通过节点中心性与最优控制策略优化信息在社交网络中的扩散,比较不同中心性指标的效果,并验证在资源有限时优先选择中心节点的策略。

摘要:

我们把信息传播建模为易感-感染流行病过程,并提出一个联合优化问题,以在固定持续时间内最大化信息扩散。网络中的个体根据其中心性指标分组,每个组在宣传期间受到外部控制函数(通过广告)的影响。目标是最大化一个线性组合的目标函数,包括截止日期时被通知个体比例的奖励和整个宣传活动期间应用控制(广告)的总成本。我们还研究了一个具有固定预算约束的变体问题。我们使用最优控制理论中的庞特里亚金最大值原理建立了最优性系统,并使用前向-后向扫描技术进行数值求解。我们的方法允许我们比较不同中心性指标(PageRank、度数、接近度和中介中心性)在最优控制框架中最大化信息传播的效果。我们发现,度数——一个简单且局部的指标——在科学合作、Slashdot和Facebook三个社交网络上表现良好。最优策略在资源稀缺时优先选择中心节点,但在资源充足时则选择非中心节点。我们的框架具有通用性,可用于其他疾病或信息传播模型的研究——这些模型可以使用常微分方程系统进行建模——对于具有已知邻接矩阵的网络。

英文摘要:

We model information dissemination as a susceptible-infected epidemic process and formulate a problem to jointly optimize seeds for the epidemic and time varying resource allocation over the period of a fixed duration campaign running on a social network with a given adjacency matrix. Individuals in the network are grouped according to their centrality measure and each group is influenced by an external control function---implemented through advertisements---during the campaign duration. The aim is to maximize an objective function which is a linear combination of the reward due to the fraction of informed individuals at the deadline, and the aggregated cost of applying controls (advertising) over the campaign duration. We also study a problem variant with a fixed budget constraint. We set up the optimality system using Pontryagin's Maximum Principle from optimal control theory and solve it numerically using the forward-backward sweep technique. Our formulation allows us to compare the performance of various centrality measures (pagerank, degree, closeness and betweenness) in maximizing the spread of a message in the optimal control framework. We find that degree---a simple and local measure---performs well on the three social networks used to demonstrate results: scientific collaboration, Slashdot and Facebook. The optimal strategy targets central nodes when the resource is scarce, but non-central nodes are targeted when the resource is in abundance. Our framework is general and can be used in similar studies for other disease or information spread models---that can be modeled using a system of ordinary differential equations---for a network with a known adjacency matrix.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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