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现代复杂的通信网络内部存在着广泛的幂律现象,网络节点之间存在相关特性.根据这种相关特性,提出了网络不动点理论.将Banach不动点理论引入网络模型,证明了网络不动点理论的正确有效性.证明过程是把通信网络看作由路径预测算法产生的似马尔可夫链的路由节点迭代序列形成的网络空间.由节点相关性可知,此空间中的节点序列相对越长就越能折射出搜索的目标所在,预测准确率也会逐步增加,可以更好地进行目标定位、数据挖掘等.通过某种路由准则的算子从源节点最终映射到的目的节点与Banach空间的不动点相对应,即为网络空间的不动点.当网络发展到能为用户提供真正的无处不在的连接时,网络不动点理论的物理特性将非常明显.因为网络规模越大,节点间的群体作用越显著,就越能显现网络不动点理论的物理特性.
There exist extensive power-law phenomena in modern complicated communication networks, and there are some characteristics between network nodes.According to the related characteristics, a fixed-point theory of network is proposed.The Banach fixed-point theory is introduced into the network model to prove that the network is not The correctness of the moving point theory is proved by the proof that the communication network is regarded as the network space formed by the iterative sequence of routing nodes based on the Markov chain generated by the path prediction algorithm.The node correlation shows that the node sequence in this space is relatively The longer it can reflect the search target, the prediction accuracy will gradually increase, you can better target location, data mining, etc. Through a routing algorithm operator from the source node to the final mapping of the destination node and The fixed point of Banach space corresponds to the fixed point of cyberspace.The physical characteristics of the fixed point theory of the network will be very obvious when the network is developed to provide a true ubiquitous connection to the user.Because the network size The larger, the more significant the role of the group between nodes, the more able to show the physical characteristics of the network fixed point theory.