Dealing with data on uncertainty has appealed to many researchers as there may be many stochastic problems in a realistic situation. In this paper, we study two basic uncertainty models: Existential Uncertainty Model where the location of each node is fixed while it may be absent with some probability, and the Locational Uncertainty Model where each node must be present, but the situation is uncertain. We consider the problem of estimating the expectation and the tail bound distribution of the diameter, and obtain an improved FPRAS (Fully Polynomial Randomized Approximation Scheme) which requires much fewer samples. In the meanwhile, we prove some problems in the two uncertainty models can't be approximated within any factor unless NP C BPP by simple reductions.
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机译：处理有关不确定性的数据已经上诉许多研究人员，因为在现实情况下可能存在许多随机问题。在本文中，我们研究了两个基本的不确定性模型：存在每个节点的位置的存在性不确定性模型，而可能存在一些概率，以及必须存在每个节点的位置不确定性模型，但情况是不确定的。我们考虑估计直径的期望和尾部边界分布的问题，并获得改进的FPRA（完全多项式随机近似方案），其需要更少的样品。同时，我们证明了两个不确定性模型中的一些问题在任何因素中都无法近似，除非通过简单地减少NP C BPP。
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