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arXiv 1507.03328cs.SI
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传统营销与病毒式营销相结合实现两栖影响力最大化

Combining Traditional Marketing and Viral Marketing with Amphibious Influence Maximization

Wei Chen, Fu Li, Tian Lin, Aviad Rubinstein

摘要:

在本文中,我们提出了两栖影响力最大化(AIM)模型,结合传统的营销通过内容提供方和病毒式营销的消费者在社交网络在一个单一的框架。在AIM中,一组内容提供方和消费者形成了一个二分网络,而消费者也形成了他们的社会网络,影响力从内容提供方传播到消费者,并在社会网络中的消费者之间传播,遵循独立的级联模型。广告商需要选择种子内容提供方的子集和种子消费者的子集,使得来自种子提供方的影响力通过种子消费者可以到达社交网络中预期的大量消费者。我们证明了AIM问题是NP-困难的,通过减少从Feige的k-证明证明系统3-SAT 5的任何常数因子内近似。我们也给出了证据,即使当社会网络图是平凡的(即没有边),多项式时间常数因子近似AIM是不可能的。然而,当我们假设描述内容提供方对消费者的影响的加权双邻接矩阵是恒定的秩时,这是推荐系统中经常使用的一个常见假设,我们提供了一个多项式时间算法,该算法实现了$(1-1/e-ε)^3$对于任何(多项式小)$ε> 0$的近似比。我们的算法结果仍然适用于一个更一般的模型,其中社会网络中的级联遵循一般的单调和次模函数。

英文摘要:

In this paper, we propose the amphibious influence maximization (AIM) model that combines traditional marketing via content providers and viral marketing to consumers in social networks in a single framework. In AIM, a set of content providers and consumers form a bipartite network while consumers also form their social network, and influence propagates from the content providers to consumers and among consumers in the social network following the independent cascade model. An advertiser needs to select a subset of seed content providers and a subset of seed consumers, such that the influence from the seed providers passing through the seed consumers could reach a large number of consumers in the social network in expectation. We prove that the AIM problem is NP-hard to approximate to within any constant factor via a reduction from Feige's k-prover proof system for 3-SAT5. We also give evidence that even when the social network graph is trivial (i.e. has no edges), a polynomial time constant factor approximation for AIM is unlikely. However, when we assume that the weighted bi-adjacency matrix that describes the influence of content providers on consumers is of constant rank, a common assumption often used in recommender systems, we provide a polynomial-time algorithm that achieves approximation ratio of $(1-1/e-ε)^3$ for any (polynomially small) $ε> 0$. Our algorithmic results still hold for a more general model where cascades in social network follow a general monotone and submodular function.

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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