最大化基于影响力的群体Shapley中心性
Maximizing Influence-based Group Shapley Centrality
摘要：
网络分析中的一个关键问题是所谓的影响最大化问题，其在于在社交网络中找到至多$k$种子用户的集合$S$，从而最大化来自$S$的信息的传播。本文研究了一个相关的，但略有不同的问题：我们要找到一个集合$S$的最多$k$种子用户，最大限度地传播信息，当$S$被添加到一个已经预先存在的，但未知的种子用户集$T$。我们认为这是一个非常现实的情况。假设中央实体想要传播一条新闻，同时具有影响$k$用户的预算。这个中央权威机构可能知道一些用户已经知道了这些信息，并且无论如何都会传播它。然而，这些用户的身份完全未知。我们使用组Shapley值，合作博弈论的一个有充分依据的概念来模拟这个优化问题。虽然标准的影响最大化问题是很容易近似的任何$ε>0$的一个因素$1-1/e-ε$，假设共同的计算复杂性的结构，我们得到了很强的硬度的近似结果的问题在本文中。也许最突出的是，我们表明，它不能近似在$1/n^{o(1)}$下的间隙指数时间假设。因此，不太可能实现比多项式因子近似更好的任何东西。然而，我们表明，贪婪算法可以实现任何$ε>0$的$\frac{1-1/e}{k}-ε$的一个因素，并不是所有的设置中丢失的$k$有界。
英文摘要：
One key problem in network analysis is the so-called influence maximization problem, which consists in finding a set $S$ of at most $k$ seed users, in a social network, maximizing the spread of information from $S$. This paper studies a related but slightly different problem: We want to find a set $S$ of at most $k$ seed users that maximizes the spread of information, when $S$ is added to an already pre-existing - but unknown - set of seed users $T$. We consider such scenario to be very realistic. Assume a central entity wants to spread a piece of news, while having a budget to influence $k$ users. This central authority may know that some users are already aware of the information and are going to spread it anyhow. The identity of these users being however completely unknown. We model this optimization problem using the Group Shapley value, a well-founded concept from cooperative game theory. While the standard influence maximization problem is easy to approximate within a factor $1-1/e-ε$ for any $ε>0$, assuming common computational complexity conjectures, we obtain strong hardness of approximation results for the problem at hand in this paper. Maybe most prominently, we show that it cannot be approximated within $1/n^{o(1)}$ under the Gap Exponential Time Hypothesis. Hence, it is unlikely to achieve anything better than a polynomial factor approximation. Nevertheless, we show that a greedy algorithm can achieve a factor of $\frac{1-1/e}{k}-ε$ for any $ε>0$, showing that not all is lost in settings where $k$ is bounded.
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