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     

超立方体系统中基于安全通路向量的容错路由

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.针对系统中存在链路故障的情况,提出了用于记录最优通路的安全通路向量(safety path vectors,简称SPVs)概念,并给出了建立SPVs及其容错路由算法.其中SPVs的赋值可以通过n-1轮邻节点之间的信息交换来完成,且算法中各节点的存储开销仅为n bits,因此,SPVs是安全向量(SVs)与扩展安全向量(ESVs)的一种扩展,具有比SVs和ESVs更好的记录最优通路的能力.另外，与基于最优通路矩阵(optimal path matrices,简称OPMs)及扩展最优通路矩阵(extended optimal path matrices,简称EOPMs)的容错路由算法相比,SPVs呈指数级地降低了算法的存储开销，且能够记录OPMs和EOPMs所不能记录到的最优通路信息.理论分析和仿真实验验证了SPVs的上述性能.     

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。     

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。     

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.     

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     

局部扭曲立方体单播容错路由算法

在n维局部扭曲立方体存在节点故障的情况下,基于路由能力的概念提出了一种单播容错路由算法,该算法首先寻找最短路径上满足路由能力值要求的邻接节点,其次寻找非最短路径上满足路由能力值要求的邻接节点。这样求得的容错路径首先是最优路径,其次为次优路径。     

基于局部信息的单播容错路由算法

对n维局部扭曲立方体存在边故障的情况下,基于局部信息的思想,通过存储其邻接节点的边故障信息数组并引入消息回溯机制,设计了一种单播容错路由算法。仿真实验表明,当有大量的边发生故障时,该算法也能成功地实现消息传递。     

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。     

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。     

A Fault-Tolerant and Heuristic Routing Algorithm for Faulty Hypercubes

A fault-tolerant and heuristic routing algorithm for faulty hypercube systems is described.To improve the efficiency,the algorithm adopts a heuristic backtracking strategy and each node has an array to record its all neighbors‘ faulty link information to avoid unnecessary searching for the known faulty links.Furthermore,the faulty link information is dynamically accumulated and the technique of heuristically searching for optimal link is used.The algorithm routes messages through the minimum feasible path between the sender and receiver if at least one such path exists,and takes the optimal path with higher probability when faulty links exist in the faulty hypercube.     

A fault tolerant routing algorithm based on cube algebra for hypercube systems

We propose an approach to determine the shortest path between the source and the destination nodes in a faulty or a non-faulty hypercube. The number of faulty nodes and links may be rather large and if any path between the nodes exists, the developed algorithm determines it. To construct this algorithm, some properties of the cube algebra are considered and some transformations based on this algebra are developed.     

The Flexible Hypercube: A New Fault-Tolerant Architecture for Parallel Computing

This paper presents the new Flexible Hypercube architecture. The Flexible Hypercube is a fault-tolerant network topology that can be constructed for an arbitrary number of nodes and is incrementally expandable. This topology maintains the strong features of the Hypercube while overcoming deficiencies in expandability. It is shown to have strong node connectivity, a small diameter, and to be tolerant of faults. The Flexible Hypercube is a suitable architecture for the design of both tightly coupled parallel systems and distributed systems. Efficient fault-free and fault-tolerant algorithms for message routing and broadcasting are presented for the architecture. The fault-free algorithm guarantees successful routing inO(logN) time, whereNis the number of nodes in the system, and the fault-tolerant algorithm guarantees routing to functioning nodes if a route exists. The fault-free and fault-tolerant broadcasting algorithms have time complexityO(logN), and the fault-tolerant algorithm guarantees success if no two faulty nodes are adjacent and no functioning node is adjacent to two faults.     

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     

超立方体网络中路由生成算法的子立方分裂方法

超立方,子立方,路由,分布式,容错     

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。     

A fast pessimistic diagnosis algorithm for generalized hypercube multicomputer systems

The reliability of processors is an important issue for designing a massively parallel processing system for which fault-tolerant computing is crucial. In order to achieve high system reliability and availability, a faulty processor (node) when found should be replaced by a fault-free processor. Within a multiprocessor system, the technique of identifying faulty nodes by constructing tests on the nodes and interpreting the test outcomes is known as system-level diagnosis. The topological structure of a multicomputer system can be modeled by a graph of which the vertices and edges correspond to nodes and links of the system, respectively. This work presents a system-level diagnosis algorithm for a generalized hypercube which is an attractive variance of a hypercube. The proposed algorithm is based on the PMC model and can isolate all faulty nodes to within a set which contains at most one fault-free node. If the total number of nodes to be diagnosed in a generalized hypercube is N, the proposed algorithm can run in O(Nlog?N) time, and being superior to Yang??s algorithm proposed in 2004, it can diagnose not only a hypercube but also a generalized hypercube.     

Fault-tolerant routing in mesh architectures

It is important for a distributed computing system to be able to route messages around whatever faulty links or nodes may be present. We present a fault-tolerant routing algorithm that assures the delivery of every message as long as there is a path between its source and destination. The algorithm works on many common mesh architectures such as the torus and hexagonal mesh. The proposed scheme can also detect the nonexistence of a path between a pair of nodes in a finite amount of time. Moreover, the scheme requires each node in the system to know only the state (faulty or not) of each of its own links. The performance of the routing scheme is simulated for both square and hexagonal meshes while varying the physical distribution of faulty components. It is shown that a shortest path between the source and destination of each message is taken with a high probability, and, if a path exists, it is usually found very quickly