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All-terminal hypernetwork reliability synthesis of a kind of semi-deterministic hypergraphs
International Journal of Modern Physics C ( IF 1.9 ) Pub Date : 2021-06-23 , DOI: 10.1142/s0129183121501539
Ke Zhang 1, 2 , Haixing Zhao 3 , Zhonglin Ye 3 , Wenjun Hu 1, 2 , Minmin Miao 1, 2
Affiliation  

Network reliability plays an important role in analysis, synthesis and detection of real-world networks. In this paper, we first propose the concept of hypernetwork reliability, which generalizes the concept of network reliability. The model for hypernetwork reliability studies consists of a hypergraph with perfect reliable vertices and equal and independent hyperedge failure probability 1p. The measure of reliability is defined as the probability that a hypergraph is connected. Let H be an r-uniform hypergraph with the number of vertices n and the number of hyperedges m, where every hyperedge connects r vertices. We confirm the possibility of the existence of a fixed hypergraph that is optimal or least for all hyperedges same survival possible p. It is simple to verify that such hypergraph exists if m=[n1r1]. For a kind of 2-regular 3-uniform hypergraphs, we calculate the upper and lower bounds on the all-terminal reliability, and describe the class of hypergraphs that reach the boundary.

中文翻译:

一种半确定性超图的全端超网络可靠性综合

网络可靠性在现实世界网络的分析、综合和检测中起着重要作用。在本文中,我们首先提出了超网络可靠性的概念,它概括了网络可靠性的概念。超网络可靠性研究模型由具有完美可靠顶点和相等且独立的超边失效概率的超图组成1-p. 可靠性的度量定义为超图连接的概率。让H豆角,扁豆r- 具有顶点数的均匀超图n和超边的数量, 每个超边都连接r顶点。我们确认存在一个固定超图的可能性,该超图对于所有超边来说都是最优的或最少的p. 验证这样的超图是否存在很简单,如果=[n-1r-1]. 对于一种2-正则3-均匀超图,我们计算了全端可靠性的上下界,并描述了到达边界的超图的类别。
更新日期:2021-06-23
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