In this paper, we study a problem of detecting the source of diffused information by querying individuals, given a sample snapshot of the information diffusion graph, where two queries are asked: (i) whether the respondent is the source or not, and (ii) if not, which neighbor spreads the information to the respondent. We consider the case when respondents may not always be truthful and some cost is taken for each query. Our goal is to quantify the necessary and sufficient budgets to achieve the detection probability 1−δ1-\delta for any given 0<δ<10< \delta < 1 . To this end, we study two types of algorithms: adaptive and non-adaptive ones, each of which corresponds to whether we adaptively select the next respondents based on the answers of the previous respondents or not. We first provide the information theoretic lower bounds for the necessary budgets in both algorithm types. In terms of the sufficient budgets, we propose two practical estimation algorithms, each of non-adaptive and adaptive types, and for each algorithm, we quantitatively analyze the budget which ensures 1−δ1-\delta detection accuracy. This theoretical analysis not only quantifies the budgets needed by practical estimation algorithms achieving a given target detection accuracy in finding the diffusion source, but also enables us to quantitatively characterize the amount of extra budget required in non-adaptive type of estimation, referred to as adaptivity gap. We validate our theoretical findings over synthetic and real-world social network topologies.

中文翻译：

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网络信息源查找：预算查询


在本文中，我们研究了通过查询个人来检测扩散信息源的问题，给定信息扩散图的样本快照，其中提出两个查询：（i）受访者是否是信息源，以及（ii） ）如果不是，哪个邻居将信息传播给受访者。我们考虑这样的情况：受访者可能并不总是诚实，并且每次查询都会产生一些成本。我们的目标是量化必要且足够的预算，以实现任何给定 0<δ<10< \delta < 1 的检测概率 1−δ1-\delta 。为此，我们研究了两种类型的算法：自适应算法和非自适应算法，每种算法都对应于我们是否根据先前受访者的答案自适应地选择下一个受访者。我们首先提供两种算法类型中必要预算的信息论下限。在充足的预算方面，我们提出了两种实用的估计算法，分别是非自适应和自适应类型，并且对于每种算法，我们定量分析了确保 1−δ1-\delta 检测精度的预算。这种理论分析不仅量化了实际估计算法在寻找扩散源时实现给定目标检测精度所需的预算，而且使我们能够定量表征非自适应类型估计（称为自适应性）所需的额外预算量差距。我们通过合成和现实世界的社交网络拓扑验证了我们的理论发现。