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.     

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。     

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.     

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。     

Embedding Hamiltonian Cycles into Folded Hypercubes with Faulty Links

It has been known that an n-dimensional hypercube (n-cube for short) can always embed a Hamiltonian cycle when the n-cube has no more than n−2 faulty links. In this paper, we study the link-fault tolerant embedding of a Hamiltonian cycle into the folded hypercube, which is a variant of the hypercube, obtained by adding a link to every pair of nodes with complementary addresses. We will show that a folded n-cube can tolerate up to n−1 faulty links when embedding a Hamiltonian cycle. We present an algorithm, FT_HAMIL, that finds a Hamiltonian cycle while avoiding any set of faulty links F provided that |F|⩽n−1. An operation, called bit-flip, on links of hyper-cube is introduced. Simple yet elegant, bit-flip will be employed by FT_HAMIL as a basic operation to generate a new Hamiltonian cycle from an old one (that contains faulty links). It is worth pointing out that the algorithm is optimal in the sense that for a folded n-cube, n−1 is the maximum number for |F| that can be tolerated, F being an arbitrary set of faulty links.     

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。     

Distributed computing on oriented anonymous hypercubes with faulty components

We give efficient algorithms for distributed computation on oriented, anonymous, asynchronous hypercubes with possible faulty components (i.e. processors and links) and deterministic processors. Initially, the processors know only the size of the network and that they are inter-connected in a hypercube topology. Faults may occur only before the start of the computation (and that despite this the hypercube remains a connected network). However, the processors do not know where these faults are located. As a measure of complexity we use the total number of bits transmitted during the execution of the algorithm and we concentrate on giving algorithms that will minimize this number of bits. The main result of this paper is an algorithm for computing Boolean functions on anonymous hypercubes with bit cost , where is the number of faulty components (i.e. links plus processors), is the number of links which are either faulty, or non-faulty but adjacent to faulty processors, and is the diameter of the hypercube with faulty components. Received: October 1992 / Accepted: April 2001     

Near-optimal message routing and broadcasting in faulty hypercubes

A distributed routing algorithm for faulty hypercubes is described. This algorithm uses a directed depth-first approach to find a path between the sender and receiver of a message whenever at least one non-faulty path exists. We show that, when an arbitrary number of elements of the hypercube can be faulty, the algorithm always routes messages using fewer than 2N hops, whereN is the number of nodes in the hypercube. This performance is shown to be within a factor of two of the optimal worst-case routing efficiency. Through foult simulations, we show that, even when up to half of the elements in the cube are faulty, complete the analysis, we prove that our algorithm is deadlock-free. Finally, we present two extensions of the algorithm. The first uses local storage to reduce the overhead of the algorithm while the second allows reliable broadcasting in the presence of an arbitrary number of faults.Supported in part by the National Science Foundation under Grant CCR-9010547.Supported in part by the National Science Foundation Instrumentation Grant CDA-8820627.     

基于比较诊断模型的超立方网络诊断算法

一个有效的诊断算法对多处理器系统而言极其重要。在多处理器系统中,识别所有故障节点的能力称为诊断系统的诊断度。在比较模型下,诊断 的执行是通过一个比较器处理器,给与之相邻的一对处理器发送相同的输入信号,并比较两者间的响应状态。为了提高超立方网络的诊断度,提出了一种新型的基于比较模型的超立方故障诊断算法,其利用超立方网络节点连接的特性生成一个拓扑图ES(k;n),最终得出一个3位二进制的诊断症候集,从而确定系统故障节点。该算法的诊断度最优能达到4n,大于传统超立方的诊断度n。     

A reconfigurable modular fault-tolerant hypercube architecture

We propose a new fault-tolerant design of a hypercube system. We first build the fault-tolerant modules (FTM's), then we interconnect these FTM's as the modular hypercube. Finally, we obtain our proposed system by augmenting links, called the spare-sharing links (SSL's), in the modular hypercube, which forms a ring connection in our architecture. The characteristic of our system is that the spare nodes in an FTM can be used as local spares to replace the faulty nodes in the FTM, or as remote spares to replace the faulty nodes in other FTM's via the spare-sharing links in the architecture. Thus, the use of spare nodes in any FTM will increase, and the proposed system reliability will improve. In the system, the switch and link failures are also considered. The modular diagnosis and modular reconfiguration are proposed to identify and reconfigure the failure of nodes, switches, and links     

自适应蚁群算法的移动机器人路径规划

针对传统蚁群算法在路径规划中存在收敛速度和寻优能力不平衡，算法易陷入局部最优等问题，提出一种自适应改进蚁群算法。为了提高算法收敛速度，在栅格环境下，根据最优路径的特点以及实际环境地图的基本参数，对初始信息素进行差异化分配；为了提高蚂蚁搜索效率，在状态转移概率中引入转角启发信息并对路径启发信息进行改进；重新制定信息素更新策略，设定迭代阈值，调整信息素挥发系数和信息素浓度，使算法在迭代后期依然具有较强的搜索最优解能力；采用分段三阶贝塞尔曲线对最优路径进行平滑处理以满足机器人实际运动要求。通过实验仿真与其他算法进行对比分析，验证了改进算法的可行性、有效性和优越性。     

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。     

Reliable Communication on Cube-Based Multicomputers

We consider a distributed unicasting algorithm for hypercubes with faulty nodes(including disconnected hypercubes)using the safety level concept.The safety level of ach node in an n-dimensional hypercube in an approximated measure of the number and distribution of faulty nodes in the neighborhood and it can be easily calculated through n-1 rounds of information exchange among neighboring nodes.Optimal unicasting between two nodes is guaranteed if the safety level of the source node is no less than the Hamming distance between the source and the destination.The feasibility of an optimal or suboptimal unicasting can be easily determined at the source node by comparing its safety level,together with its neighbors‘ safety levels,with the Hamming distance between the source and the destination.The proposed scheme is also the first attempt to address the unicasting problem in discronnected hypercubes.The safety level concept is also extended to be used in hypercubes with both faulty nodes and links and in generalized hypercubes.     

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     

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.     

All-to-all broadcast and matrix multiplication in faulty SIMDhypercubes

In this paper, we develop algorithms in order of efficiency for all-to-all broadcast problem in an N=2ⁿ-node n-dimensional faulty SIMD hypercube, Q_n, with up to n-1 node faults. The algorithms use a property of a certain ordering of dimensions. Our analysis includes startup time (α) and transfer time (β). We have established the lower bound for such an algorithm to be nα+(2N-3)Lβ in a faulty hypercube with at most n-1 faults (each node has a value of L bytes). Our best algorithm requires 2nα+2NLβ and is near-optimal. We develop an optimal algorithm for matrix multiplication in a faulty hypercube using all-to-all broadcast and compare the efficiency of all-to-all broadcast approach with broadcast approach and global sum approach for matrix multiplication. The algorithms are congestion-free and applicable in the context of available hypercube machines     

Virtual network mapping algorithm in the cloud infrastructure

Network virtualization has received considerable attention recently because a Cloud Provider (CP) that is responsible for deploying a substrate network in the cloud infrastructure uses network virtualization to support multiple Virtual Network (VN) requests over the shared substrate network. However, mapping multiple VN requests with constraints on virtual nodes and virtual links into a shared substrate network presents a significant challenge, and is considered an NP-hard problem. In this paper, we propose a heuristic mapping algorithm that handles online VN requests. The node mapping algorithm selects a substrate node for mapping that satisfies both a virtual node's resource requirement and its amount of requested bandwidth. The link mapping algorithm either maps a virtual link to the shortest substrate path that satisfies the requested bandwidth of the virtual link or uses the cut-shortest path approach to map a virtual link to multiple substrate paths that satisfy the requested bandwidth of the virtual link. The path migration algorithm migrates virtual links to different substrate paths to maximize the number of accepted VN requests in a substrate network. Simulation results show that the proposed heuristic mapping algorithm uses resources more efficiently, produces more revenue, and has better performance than existing mapping approaches.     

交换超立方网中的最短路径路由算法

针对交换超立方网络的最短路由问题,提出一个交换超立方网中的最短路径路由算法.利用图论的方法,通过引进子网的概念,研究交换超立方网的拓扑性质,给出节点各边可进行最短路径路由的充要条件,得到其时间复杂度为O(s+t)2).理论分析和仿真结果表明,该算法可输出交换超立方网中任意两节点间的一条最短路径.     

基于改进势场蚁群算法的机器人路径规划

提出一种全局静态环境下移动机器人路径规划的改进势场蚁群算法.该算法采用人工势场法求得的初始路径和机器人与下一个节点之间的距离综合构造启发信息,并引入启发信息递减系数,避免了传统蚁群算法由于启发信息误导所致的局部最优问题;依据零点定理, 提出初始信息素不均衡分配原则,不同的栅格位置赋予不同的初始信息素,降低蚁群搜索的盲目性,提高算法的搜索效率;设定迭代阈值,自适应调节信息素挥发系数,使得该算法具有较高的全局搜索能力,避免出现停滞现象.仿真结果验证了所提出算法的可行性和有效性.     

基于选择函数的分布式启发算法DCLC—DSF

QoS路由的DCLC单播路由（Delay-Constrained Least-Cost Unicast Routing）问题属于NP－完全问题。本文提出一种多项式复杂度的分布式启发算法DCLC－DSF。DCLC－DSF基于简单的选择函数,每个网络结点只需维持本地的状态信息：相邻链路的延时和代价度量。该算法有以下优点：1）简单性;2）动态性;3）重路由功能;4）协商功能。在最坏情况下,DCLC－DSF的消息复杂度为O（e^2）,结点的计算复杂度为O（n^2）;在稳定的网络环境下,消息复杂度为O（e）。此外,本文还给出DCLC－DSF算法有限状态机模型。仿真实验表明：DCLC－DSF算法的平均代价不精确度是最佳算法的5－8％,证明它是一种简单、精确、健壮的的启发式算法。