Mesh网络容错广播路由算法的概率分析

One-to-all or broadcast communication is one of the most important communication patterns and occurs in many important applications in parallel computing. This paper proposes a fault tolerant, local-irdormation-based, and distributed broadcast routing algorithm based on the concept of k-submesh-cormectivity in all-port mesh networks.The paper analyzes the fault tolerance of the algorithm in terms of node failure probability. Suppose that every nodehas independent failure probability, and deduce the success probability of the broadcast routing, which successfully routes a message from a source node to all non-faulty nodes in the networks. The paper strictly proves that the broadcast routing algorithm with the success probability of 99％ to route among all non-faulty nodes on mesh networks with forty thousand nodes, in case that the node failure probability is controlled within 0.12％ Simulation results show that the algorithm is practically efficient and effective, and the time steps of the algorithm are very closeto the optimum.     

点对点网络容错路由算法的概率分析

基于网络中结点错误概率 ,提出一种新的概率分析方法 ,对网络中点对点的路由算法的容错性概率、路径长度、算法复杂性进行严格的推导 .以超立方体网络为分析的网络拓扑 ,提出在其上的一个路由算法 .分析表明 :在所有实际规模的超立方体网络中 (其结点数可以高达十亿个 ) ,在相当大的结点出错概率 (可高达 8% )的情况下 ,路由算法可达到 99.9%的成功概率     

交换超立方体网络容错路由研究

为了研究交换超立方体网络容错路由问题,引入了相邻结点集合类的概念,提出了相邻结点集的求解公式。对于满足任意子连通性条件的交换超立方体网络,给出了基于相邻结点集合类的自适应容错路由算法及算法的步长上界。仿真实验结果表明算法是有效的。     

超立方体网络下的自适应容错路由研究*

针对超立方体结构的多处理机系统出现故障的问题,对容错超立方体网络的局部连通性进行了研究。根据局部连通性的特点定义了相邻节点集合类的概念,提出并证明了求解两类相邻节点集合的公式。给出了满足任意子连通性条件的超立方体网络的自适应容错路由算法。该算法是分布式和基于局部信息的,可以预防死锁。仿真实验的结果表明算法是高效的,且构建的路径长度接近于最优路径长度。     

具有大量错误结点的超立方体网络中的高效路由算法的设计与讨论

该文提出了容错超立方体网络的一个很自然的机关报概念;局部连通性;讨论了两种类型的局部连通性;大局中部k-维子立方体连通性和局部子立方体连通性;一个局部连通的超立方体网络可容许大量错误结点且能确保超立方体网络是全局连通的;给出了满足局部连通性条件的超立方体网络中的几个高效的容错路由算法,文中的容错路由算法是分布式的和基于局部信息的,因而具有很强的实际意义。     

局部k-子立方连通的超立方网络中的广播容错算法

基于局部k-子立方体连通性的概念,提出了在局部k-子立方连通的超立方体中的,“播路由算法该算法是分布的、基于局部信息的,在容错性上有了很大的提高,能在线性时间内构造超立方体H1中接近最优的路径。     

故障超立方体网络中的高效容错路由算法研究

对超立方体网络中具有大量节点和链路故障模式进行了研究,提出了两类"子连通性"即k-维子连通性和任意子连通性的概念;基于两类子连通性概念,分别给出了两个满足该两类子连通性条件的超立方体网络的分布式容错路由算法.证明了已有的两类局部连通性概念中的条件"错误节点数小于正确节点数"是不必要的.提出的两个子连通性概念是两类局部连通性概念的最大扩展,可以在更大程度上保证整个超立方体网络的全局连通性,是已有的两类局部连通性概念的一种完全扩展.     

网络容错路由算法概率分析的一种新的方法

该文提出了一种新的概率分析方法来研究在给定结点错误概率的情况下超立方体网络强容错路由算法的容错性的概率。针对文中提出的基于新的局部连通性网络容错模型的高效的强容错路由算法犤1犦,该文首次严格证明了一个具有1024个结点的10维超立方体网络能够容许多达4.7%的错误结点而具有99%的概率确保找到正确结点组成的路径,而如果结点的错误概率不超过0.1%,则所有实际规模的超立方体网络能够具有99.9%的概率确保找到正确结点组成的路径。该算法的时间性能是最优的,且该算法构造的路径的长度不超过源结点和目的结点之间海明距离的两倍加上一个很小的常数。     

三维Mesh网络容错路由算法及其概率分析

基于三维Mesh网络中k-Mesh子网连通的概念提出一个简单的基于局部信息和分布式的容错路由算法，并对其容错性进行概率分析．假设每个结点具有独立的出错概率，推导出路由算法成功返回由正确结点组成的路径的概率,结果表明即使三维Mesh网络上非常简单的路由算法也有相当高的成功概率．算法的时间复杂性是线性的,所构造的路由路径长度非常接近两点间的最优路径长度．另外，基于k-Mesh子网容错模型提出的容错路由算法是基于局部信息的和分布式的，因而具有很好的实际意义．     

具有不连通子立方体的超立方体中广播路由

基于扩展的局部k—维子立方体连通的超立方体网络Hn,提出了超立方体网络Hn中新的广播容错路由算法。算法分析表明,基于扩展局部k—维子立方体连通的广播路由算法比基于局部k-子立方连通的广播路由算法提高了超立方体网络的容错性和通用性。     

基于超立方体容错路由算法分析*

基于超立方体的优良的拓扑性质,提出了一个应用于超立方体网络的容错路由算法.该容错路由算法是基于局部信息的,因为路由算法在路由过程中,只需要知道其邻节点的信息,而无须知道其他节点的出错情况.对于给定的源节点和目的节点,路由算法均能够找到一条最优容错路径,并且可以预防死锁.模拟实验结果表明,路由算法所构造的路由路径长度接近于两个节点之间的最优路径长度.     

Mesh网络路由算法容错性的概率分析

该文基于k-Mesh子网的概念提出了两个简单的基于局部信息和分布式的Mesh网络容错路由算法,并对其容错性进行概率分析;在每个结点具有独立的出错概率的假设条件下,推导出路由算法成功返回由正确结点组成的路径的概率．该文运用严格的数学推理,证明了Mesh网络结点出错概率只要控制在1．87％以内,则对于多达几十万个结点的Mesh网络,提出的路由算法具有99％的概率确保找到正确结点组成的路径．路由算法的时间复杂性是线性的．模拟结果表明路由算法所构造的路由路径长度非常接近于两结点之间的最优路径长度．     

基于子网的三维Mesh网络容错广播路由算法

在并行计算机系统中,广播通信是极为重要的通信模式之一。该文基于k-Mesh子网(子立方体)连通的概念提出一个基于局部信息和分布式的三维Mesh网络容错广播路由算法。该算法利用邻结点的状态信息,动态地构建以单个k-Mesh子网为结点的广播树,该广播树能容忍相当多的结点出错。模拟结果表明广播路由算法的广播时间步接近最优的。该算法只要求结点知道它的邻结点的状态,而无需知道整个网络状态信息,也就是说,这些算法是基于局部信息的,因而具有很好的实际意义。     

基于LIP和RSC的超立方体网络单播容错路由算法*

基于LIP和RSC的概念,提出了一个有效的超立方体网络单播容错路由算法.该算法不仅能容纳指数级的错误节点,而且算法效率也很高.     

Probabilistic analysis on mesh network fault tolerance

Mesh networks are among the most important interconnection network topologies for large multicomputer systems. Mesh networks perform poorly in tolerating faults in the view of worst-case analysis. On the other hand, such worst cases occur very rarely in realistic situations. In this paper, we study the fault tolerance of 2-D and 3-D mesh networks under a more realistic model in which each network node has an independent failure probability. We first observe that if the node failure probability is fixed, then the connectivity probability of these mesh networks can be arbitrarily small when the network size is sufficiently large. Thus, it is practically important for multicomputer system manufacture to determine the upper bound for node failure probability when the probability of network connectivity and the network size are given. We develop a novel technique to formally derive lower bounds on the connectivity probability for 2-D and 3-D mesh networks. Our study shows that these mesh networks of practical size can tolerate a large number of faulty nodes thus are reliable enough for multicomputer systems. For example, it is formally proved that as long as the node failure probability is bounded by 0.5%$0.5\%$, a 3-D mesh network of up to a million nodes remains connected with a probability larger than 99%$99\%$.     

3-维Mesh网络容错性的概率分析研究

Mesh network is very popualr and important topological structure in parallel computing. In this paper,we focus on the fault tolerance of 3-dimensional mesh. We use the probability model to analyze the fault tolerance of mesh. To simplify our analysis, we assume the failure probability of each node is independent. We partition a 3-dimensional mesh into smaller submeshes and compute the probability with which each submesh satisfies the condition we define. If each submesh satisfies the condition, then the whole mesh is connected. We then compute the probability that a 3-dimensional mesh is connected assuming each node has a failure probability p. We use mathematical methods to derive a relationship between network node failure probability and network connectivity probability. Our simulations show that 3-dimensional mesh networks can remain connected with very high probability in practice. For example, the paper formally proves that when the network node failure probability is bounded by 0.05%, 3-dimensional mesh network of more than two hundred thousand nodes remain connected with probability larger than 99%. Theoretical and experimental results show that our method is powderful technique to calculate the lower bound of the connectivity probability of mesh network.     

具有大量错误结点的超立方体网络中的单播路由算法的设计与分析

本文讨论具有大量错误结点的超立方体网络中的单播路由算法，假定Hn是一个局部3－维子立方体连通的n-维超立方体网络并且每一个基本的3－维子立方体中分别最多有1个和2个错误结点，本文提出的单播路由算法能够在线性时间找到路径长度分别为源结点和目的结点之间大约1．5倍和2倍海明距离的次优路径，我们提出的单播路由算法只需要结点知道其邻结点的状态，而无需知道整个网络信息，也就是说，该算法是基于局部信息的，因而该算法具有很强的实际意义。