局部纽立方体和交叉立方体容错性研究

发布时间：2018-05-26 14:14

  本文选题：网络拓扑结构 + 局部纽立方体　； 参考：《大连理工大学》2015年硕士论文

【摘要】：众所周知,使用图论来构建网络拓扑结构是建模常见的形式,而且已经被越来越多的学者应用到研究之中。泛圈性和路径嵌入作为衡量网络拓扑结构容错性的一项重要指标,变得越来越受学者的关注。研究容错性不仅具有很强的学术价值而且还有很大的实际意义,它可以有效地改善和优化一个大型网络出现不可预见的故障时的情况,通过合理的规划使其能够在多线路和元件同时发生故障时,仍然可以保证网络的正常使用。当网络中出现错误时,用F表示网络结构图中错误的集合。局部纽立方体LTQn和交叉立方体CQn都是超立方体Qn的变形网络结构,它们具备Qn现有的优点,同时改进了Qn的缺点,如泛圈性等。在点数一样时,它们的直径长度是Qn的一半。容错性在衡量一个拓扑结构的标准中占有很重要的比重,也引起了科学工作者对容错性研究的兴趣和重视。本文通过在n比较小的情况下进行计算机程序搜索和在n较大的情况下进行数学归纳法的方法,研究局部纽立方体网络和交叉立方体网络的容错性质,得出了下面的结论：(1)给出弱点对的概念,并得出结论：对于任意当|F|≤n-2时,对于LTQn-f中的任意两点(弱点对中的两点除外)在LTQn-f中存在一条长为1的路径连接这两点。(2)对于任意是中的任意一个正确点,在LTQn-F中存在包含点v且长为l的正确圈,其中(3)对于任意中的任意一个正确点,在中存在包含点v且长为6的正确圈。
[Abstract]:It is well known that the use of graph theory to construct network topology is a common form of modeling and has been applied to research by more and more scholars. As an important index to measure the fault tolerance of network topology, pan cycle and path embedding have been paid more and more attention by scholars. The study of fault tolerance is not only of great academic value but also of great practical significance. It can effectively improve and optimize the situation of a large network in the event of unforeseen failures. Through reasonable planning, it can ensure the normal use of the network when the multiple lines and components fail at the same time. When errors occur in the network, F is used to represent the set of errors in the network structure diagram. Both local new cube LTQn and cross cube CQn are the deformed network structure of hypercube Qn. They have the advantages of QN and improve the shortcomings of QN, such as pancyclicity, etc. When the number of points is the same, their diameter is half the length of Q _ n. Fault-tolerance plays an important role in the criterion of a topology, and it also attracts the interest and attention of scientists in the research of fault-tolerance. In this paper, the fault-tolerant properties of local and crossed cube networks are studied by means of computer program search in the case of small n and mathematical induction in the case of larger n. The following conclusion is drawn: 1) the concept of weakness pair is given, and it is concluded that for any F 鈮，

本文编号：1937526