点边失效下网络的混合可靠度研究

We are surrounded by various complex networks today, such as social networks, technological networks, communication networks and traffic networks, etc. Due to various reasons, the vertices or communicating edges in a network are likely to fail or be attacked, so that the network is greatly fragile. Therefore, based on vertex failure and edge failure, the study of reliability analysis and reliability design for the network is increasingly of great theoretical significance and important application.. This project mainly studies the mixed reliability of a network based on vertex failure and edge failure. We shall find some algorithms for counting the mixed reliability polynomial of a network. Assume that each vertex of G has the same failure probability p and each edge of G has the same failure probability q, if p tends to 0 or q tends to 1, we determine the local optimal network model and explore some measures of optimal network on different failure strategies. Finally, we characterize the optimal network and investigate the applications of mix-reliability in the network.

现实生活中，网络无处不在，如社会网络、计算机网络、通讯网络和交通网络等。由于种种原因，网络的通讯线路或站点都有可能出现故障或者遭受到攻击，从而使网络的功能降低，甚至导致整个网络瘫痪。因此，分析已知网络当点和边失效后网络的可靠性和设计最可靠或相对可靠的网络具有重要现实意义。. 本项目主要研究一个网络点和边失效（或受到攻击）下网络的混合可靠性，内容包括点边失效下网络混合可靠性算法、点边失效概率趋于0或1时网络的局部最优性；探索不同失效情形下网络混合最优性的判断准则；刻画具有最优网络或者有限极优图族，并深入研究点边失效下网络混合可靠性的应用。

课题《点边失效下网络的混合可靠度研究》是国家自然科学基金委于2016年批准给予资助项目。课题预定研究起始时间为2017年1月至2020年12月，资助金额为40万元。本项目主要研究网络在点边同时失效条件下网络可靠度的计算、最优网络的性质和最优网络的构建等，研究内容有点边失效下的网络可靠度的计算、局部最优网络特性研究和刻画、混合极优网络判定和构建、混合可靠度应用研究等四个方面。课题组集中精力对点边失效下网络的混合可靠度进行研究，完成预定研究内容的同时，发挥成员的优势和研究兴趣，适当扩充了超网络的可靠度和网络表示学习等研究内容，共完成各类研究论文30篇，已发表论文26篇，完成硕士论文7篇，完成博士论文3篇。