超立方体多处理机系统中基于扩展最优通路矩阵的容错路由

该文在高峰等文章的基础上，提出了针对超立方体结构多处理机系统的扩展最优通路矩阵（Extended Optimal Path Matrices,EOPMs）的概念，并给出了一个建立EIPMs的算法和基于EOPMs的容错路由算法，证明了基于EOPMs的容错路由算法是基于扩展安全向量（ESVs）^[13]和基于最优通路矩阵（OPMs)^[14]容错路由算法的扩展，与原文相比，该算法的存储开销与OPMs,相同，但记录的最优通路的信息，包含了原文所记录的最优通路的信息，使搜索最优通路的能力比它们有进一步的提高。     

超立方体中基于极大安全通路矩阵的容错路由

n维超立方体结构的多处理机系统在并行与分布式处理中具有良好的性能,随着多处理机系统规模的增大,系统出现链路与节点故障的概率也随之增大,因此设计容错性更强的路由算法对n维超立方体结构的多处理机系统具有重要意义.针对超立方体结构的多处理机系统中存在链路故障的情况,提出了用于最优通路记录的极大安全通路矩阵(maximum safety path matrices,简称MSPMs)这一概念,给出了一种建立MSPMs及其容错路由算法.证明了MSPMs通过n-1轮邻节点之间的信息交换,能以矩阵的形式记录最多的最优通路     

超立方体多处理机系统中基于扩展安全向量的容错路由

针对超立方体结构的多处理机系统中存在链路故障的情况,修改了吴杰提出的安全向量的概念,提出了扩展安全向量的概念,并给出了一个基于扩展安全向量的容错路由算法,与基于安全向量的路由算法相比,基于扩展安全向量的路由算法搜索最优通路的能力有了非常大的提高,即使故障数较多时,它仍能保证把绝大多数源、目的节点间有最优通路和消息沿最优通路传递。超立方体结构中各节点扩展安全向量的赋值可以通过ｎ－１轮邻接点的信息交换     

基于NPV广义超立方体最佳容错路由算法

在网络可靠性研究中,设计较好的容错路由策略、尽可能多地记录系统中最优通路信息,一直是一项重要的研究工作.超立方体系统的容错路由算法分为可回溯算法和无回溯算法.一般说来,可回溯算法的优点是容错能力强:只要消息的源节点和目的节点有通路,该算法就能够找到把消息传递到目的地的路径;其缺点是在很多情况下传递路径不能按实际存在的最短路径传递.其代表是深度优先搜索(DFS)算法.无回溯算法是近几年人们比较关注的算法.该算法通过记录各邻接节点的故障信息,给路由算法以启发信息,使消息尽可能按实际存在的最短路径传递.这些算法的共同缺点是只能计算出Hamming距离不超过n的路由.在n维超立方体系统连通图中,如果系统存在大量的故障,不少节点对之间的最短路径大于n,因此,这些算法的容错能力差.提出了一个实例说明采用上述算法将遗失60%的路由信息.另外,由于超立方体的结构严格,实际中的真正超立方体系统不多.事实上,不少的网络系统可转换为具有大量错误节点和错误边的超立方体系统.因此,研究能适应具有大量错误节点和错误边的超立方体系统的容错路由算法是一个很有实际价值的工作.研究探讨了:(1) 定义广义超立方体系统;(2) 在超立方体系统中提出了节点通路向量(NPV)概念及其计算规则;(3) 提出了中转点技术,使得求NPV的计算复杂度降低到O(n);(4) 提出了基于NPV的广义超立方体系统最佳容错路由算法(OFTRS),该算法是一种分布式的和基于相邻节点信息的算法.由于NPV记录了超立方体系统全部最优通路和次最优通路的信息,在具有大量故障的情况下,它不会遗漏任何一条最优通路和次最优通路信息,从而实现了高效的容错路由.在这一点上,它优于其他算法.     

故障超立方体网络中的路由算法

针对超立方体结构的多处理机系统中存在故障的情况,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,只需要知道邻节点的状态,而无需知道整个网络的运行情况。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通路,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径长度接近于两个节点之间的最优路径长度。     

用最优通路矩阵实现超立方体多处理机系统的容错路由

针对拓扑结构为超立方体的多处理机系统提出了最优通路矩阵（ＯＰＭ）的概念,并约出了一个基于最优通路矩阵的路由算法。存储于超产方体各节点中的最优通路矩阵记录系统中的故障信息,用于判定消息的源节点和目的节点之间是否存在最优通路（长度等于两节点间Ｈａｍｍｉｎｇ距离的通路）。对于ｎ维超方立体,每个节点所需的存储开销为ｎ＾２个字,基于最优通路矩阵的路由算法所选的通路的长度不超过两点间的Ｈａｍｍｉｎｇ距离加２。     

Torus网络中基于标志位的容错路由

针对Torus结构的多处理机系统中容错路由的问题,提出标志位概念,给出一个基于标志位的容错路由算法。存储于Torus网络中各节点的标志位记录系统中的故障信息,用于判定消息的源节点和目的节点之间是否存在最优通路。标志位的赋值可以通过与邻节点间的信息交换完成。     

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.     

基于局部扭曲立方体的单播容错路由算法

对n维局部扭曲立方体存在节点故障时,提出了一种基于节点安全级概念的单播容错路由算法。该算法除了考虑邻接节点的安全状况外,还充分利用了局部扭曲立方体自身特有的结构,使得信息尽可能沿最优路径传递。通过模拟仿真实验可知,算法具有较高的容错能力。当故障节点的数目达到或超过一半时,算法仍能保持一个相当高的容错路由成功率,且算法所选路径在多数情况下是最优路径。     

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。     

Fault-tolerant adaptive and minimal routing in mesh-connectedmulticomputers using extended safety levels

The minimal routing problem in mesh-connected multicomputers with faulty blocks is studied. Two-dimensional meshes are used to illustrate the approach. A sufficient condition for minimal routing in 2D meshes with faulty blocks is proposed. Unlike many traditional models that assume all the nodes know global fault distribution, our approach is based on the concept of an extended safety level, which is a special form of limited fault information. The extended safety level information is captured by a vector associated with each node. When the safety level of a node reaches a certain level (or meets certain conditions), a minimal path exists from this node to any nonfaulty nodes in 2D meshes. Specifically, we study the existence of minimal paths at a given source node, limited distribution of fault information, and minimal routing itself. We propose three fault-tolerant minimal routing algorithms which are adaptive to allow all messages to use any minimal path. We also provide some general ideas to extend our approaches to other low-dimensional mesh-connected multicomputers such as 2D tori and 3D meshes. Our approach is the first attempt to address adaptive and minimal routing in 2D meshes with faulty blocks using limited fault information     

Adaptive fault-tolerant routing in cube-based multicomputers usingsafety vectors

Reliable communication in cube-based multicomputers using the safety vector concept is studied in this paper. In our approach, each node in a cube-based multicomputer of dimension n is associated with a safety vector of n bits, which is an approximated measure of the number and distribution of faults in the neighborhood. The safety vector of each node can be easily calculated through n-1 rounds of information exchange among neighboring nodes. Optimal unicasting between two nodes is guaranteed if the kth bit of the safety vector of the source node is one, where k is the Hamming distance between the source and destination nodes. The concept of dynamic adaptivity is introduced, representing the ability of a routing algorithm to dynamically adjust its routing adaptivity based on fault distribution in the neighborhood. The feasibility of the proposed unicasting can be easily determined at the source node by comparing its safety vector with the Hamming distance between the source and destination nodes. The proposed unicasting can also be used in disconnected hypercubes, where nodes in a hypercube are disjointed (into two or more parts). We then extend the safety vector concept to general cube-based multicomputers     

基于扩展安全级的Torus网络容错路由算法研究

在存在故障结点的网络中如何设计最小容错路由是网络容错研究中的一个热点问题。以存在矩形故障块的二维Torus网络为例,将扩展安全级运用到Torus中,对于网络中任意一对结点,给出存在最小路径的充要条件;并且结合扩展安全级的概念,给出建立最小通路区的方法,并用实验验证了方法的可行性。研究为存在故障结点的Torus网络寻找最小容错路径提供了理论依据。     

Depth-first search approach for fault-tolerant routing in hypercubemulticomputers

Using depth-first search, the authors develop and analyze the performance of a routing scheme for hypercube multicomputers in the presence of an arbitrary number of faulty components. They derive an exact expression for the probability of routing messages by way of optimal paths (of length equal to the Hamming distance between the corresponding pair of nodes) from the source node to an obstructed node. The obstructed node is defined as the first node encountered by the message that finds no optimal path to the destination node. It is noted that the probability of routing messages over an optimal path between any two nodes is a special case of the present results and can be obtained by replacing the obstructed node with the destination node. Numerical examples are given to illustrate the results, and they show that, in the presence of component failures, depth-first search routing can route a message to its destination by means of an optimal path with a very high probability     

A simple fault-tolerant adaptive and minimal routing approach in 3-D meshes

In this paper we propose a sufficient codition for minimal routing in 3-dimensional (3-D) meshes with faulty nodes,It is based on an early work of the author on minial routing in 2-dimensional(2-D) meshes,Unlike many traditional models that assume all the nodes know global fault distribution or just adjacent fault information,our approach is based on the concept of limited global fault information,First,we propose a fault model called faulty cube in which all faulty nodes in the system are contained in a set of faulty cubes.Fault information is then distributed to limited number of nodes while it is still sufficeint to support minimal routing.The limited fault information collcted at each node is represented by a vector caaled extended safety level.The extended safety level associated with a node can be used to determine the existence of a minimal path from this node to a given destination .Specifically,we study the existence of minimal paths at a given source node,limited distribution of fault information,minimal routing,and deadlock-free and livelock-free routing.our results show that any minimal routing that is partially adaptive can be applied in our model as long as the dstination node meets a certain conditon.We also propose a dynamic planar-adaptive routing scheme that offers better fault tolerance and adaptivity than the planar-adaptive routing scheme in 3-D meshes.Our approach is the first attempt to address adaptive and minimal routing is 3-D meshes with faulty nodes using limited fault information.