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.     

Adaptive and deadlock-free routing for irregular faulty patterns inmesh multicomputer

Message routing achieves the internode communication in parallel computers. A reliable routing is supposed to be deadlock-free and fault-tolerant. While many routing algorithms are able to tolerate a large number of faults enclosed by rectangular faulty blocks, there is no existing algorithm that is capable of handling irregular faulty patterns for wormhole networks. In this paper, a two-staged adaptive and deadlock-free routing algorithm called “Routing for Irregular Faulty Patterns” (RIFP) is proposed. It can tolerate irregular faulty patterns by transmitting messages from sources or to destinations within faulty blocks via multiple “intermediate nodes.” A method employed by RIFP is first introduced to generate intermediate nodes using the local failure information. By its aid, two communicating nodes can always exchange their data or intermediate results if there is at least one path between them. RIFP needs two virtual channels per physical link in meshes     

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     

Proof that pyramid networks are 1-Hamiltonian-connected with high probability

Wu revealed in 2001 that pyramid networks are Hamiltonian-connected. This investigation demonstrates that a pyramid network with one faulty node or one faulty edge is Hamiltonian-connected, excluding some special faulty cases by building a Hamiltonian path between any two distinct nodes in it. Although a pyramid network with one fault is not Hamiltonian-connected, this study indicates that a pyramid network is 1-Hamiltonian-connected with a very high probability.     

Effective fault detection and routing scheme for wireless sensor networks

In a wireless sensor network (WSN), random occurrences of faulty nodes degrade the quality of service of the network. In this paper, we propose an efficient fault detection and routing (EFDR) scheme to manage a large size WSN. The faulty nodes are detected by neighbour node’s temporal and spatial correlation of sensing information and heart beat message passed by the cluster head. In EFDR scheme, three linear cellular automata (CA) are used to manage transmitter circuit/ battery condition/microcontroller fault, receiver circuit fault and sensor circuit fault representation. On the other hand, L-system rules based data routing scheme is proposed to determine optimal routing path between cluster head and base station. The proposed EFDR technique is capable of detecting and managing the faulty nodes in an efficient manner. The simulation results show 86% improvement in the rate of energy loss compared to an existing algorithm.     

Fault-tolerant wormhole routing for hypercube networks

We present an adaptive fault-tolerant wormhole routing algorithm for hypercubes by using 3 virtual networks. The routing algorithm can tolerate at least n−1 faulty nodes and can route a message via a path of length no more than the shortest path plus four. Previous algorithms which achieve the same fault tolerant ability need 5 virtual networks. Simulation results are also given in this paper.     

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.     

An Adaptive Routing Algorithm for WK-Recursive Topologies

This paper presents an easy and straightforward routing algorithm for WK-recursive topologies. The algorithm, based on adaptive routing, takes advantage of the geometric properties of such topologies. Once a source node S and destination node D have been determined for a message communication, they characterize, at some level l, two virtual nodes and that respectively contain S but not D and D but not S. Such virtual nodes characterize other (where is the node degree for a fixed topology) virtual nodes of the same level that contain neither S nor D. Consequently, it is possible to locate triangles whose vertices are these virtual nodes with property to share the same path, called the self-routing path, directly connecting to . When the self-routing path is unavailable to transmit a message from S to D because of deadlock, fault, and congestion conditions, the routing strategy can follow what we call the triangle rule to deliver it. The proposed communication scheme has the advantage that 1) it is the same for all three conditions; 2) each node of a WK-recursive network, to transmit messages, does not require any information about their presence or location. Furthermore, this routing algorithm is able to tolerate up to faulty links. Received: July 19, 1998; revised May 17, 1999     

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。     

多传感器网络中的分布式故障检测算法

在传感器网络中,分布式故障检测算法(DFD算法)通过与所有邻居节点的传感器数据的比较判断,实现节点传感器的故障检测。但是,在故障节点聚集的网络区域,故障节点比例的上升将导致该区域的故障检测精度显著下降。针对多传感器网络,本文利用多传感器在相同区域的故障分布差异及传感器之间关联特性对DFD故障检测算法进行改进,提出适用于多传感器网络的MDFD算法,提高了故障聚集区域的检测精度。性能分析和仿真结果表明:在节点故障率高的网络中,与DFD和IDFD算法相比,MDFD提高了故障检测精度,算法适用于节点分布稀疏和传感器故障率较高的网络。     

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。     

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.     

Unicast in hypercubes with large number of faulty nodes

Unicast in computer/communication networks is a one-to-one communication between a source node s and a destination node t. We propose three algorithms which find a nonfaulty routing path between s and t for unicast in the hypercube with a large number of faulty nodes. Given the n-dimensional hypercube H_n and a set F of faulty nodes, node uϵ H_n is called k-safe if u has at least k nonfaulty neighbors. The H_n is called k-safe if every node of H_n is k-safe. It has been known that for 0⩽k⩽n/2, a k-safe H_n is connected if |F|⩽2^k(n-k)-1. Our first algorithm finds a nonfaulty path of length at most d(s,t)+4 in O(n) time for unicast between 1-safe s and t in the H_n with |F|⩽2n-3, where d(s,t) is the distance between s and t. The second algorithm finds a nonfaulty path of length at most d(s,t)+6 in O(n) time for unicast in the 2-safe H_n with |F|⩽4n-9. The third algorithm finds a nonfaulty path of length at most d(s,t)+O(k²) in time O(|F|+n) for unicast in the k-safe H_n with |F|⩽2^k(n-k)-1 (0⩽k⩽n/2). The time complexities of the algorithms are optimal. We show that in the worst case, the length of the nonfaulty path between s and t in a k-safe H_n with |F|⩽2^k(n-k)-1 is at least d(s,t)+2(k+1) for 0⩽k⩽n/2. This implies that the path lengths found by the algorithms for unicast in the 1-safe and 2-safe hypercubes are optimal     

One-to-one communication in twisted cubes under restricted connectivity

The dimensions of twisted cubes are only limited to odd integers. In this paper, we first extend the dimensions of twisted cubes to all positive integers. Then, we introduce the concept of the restricted faulty set into twisted cubes. We further prove that under the condition that each node of the n-dimensional twisted cube TQ_n has at least one fault-free neighbor, its restricted connectivity is 2n − 2, which is almost twice as that of TQ_n under the condition of arbitrary faulty nodes, the same as that of the n-dimensional hypercube. Moreover, we provide an O(NlogN) fault-free unicast algorithm and simulations result of the expected length of the fault-free path obtained by our algorithm, where N denotes the node number of TQ_n. Finally, we propose a polynomial algorithm to check whether the faulty node set satisfies the condition that each node of the n-dimensional twisted cube TQ_n has at least one fault-free neighbor.     

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     

一种基于动态跳数距离的有洞无线传感器网络定位方法

在无线传感器网络中,与距离无关的定位技术一直是一项挑战性的工作。尤其是在有洞的各向异性网络中,多}L节点之间的距离估算更是一个难点。针对有洞的无线传感器网络,提出一种新的距离无关定位方法,该方法可以较好地估算未知节点到参考节点之间的距离。其主要思想是,先佑算各信标节点对之间的平均单跳距离,然后选择平均单跳距离较大并且最短路径通过未知节点的信标节点对作为参考节点来估算未知节点的位置。新算法能够较好地滤除距离估算误差较大的信标节点作为参考节点。实验表明,新算法比以前的算法定位更准确。     

基于裂痕故障块的自适应容错路由表算法

基于裂痕故障块的二维网格自适应容错路由算法是一种有效的容错算法,不仅能够解决活锁问题,而且克服了传统故障块模型中状态良好的节点不能参与路由的缺陷,但同时具有明显的缺点：每次路由到以故障块边界节点为根节点的内部树时,都需要遍历此内部树,因此算法的路由长度并不是最短的。针对上述问题,提出基于裂痕故障块的自适应容错路由表算法,其中路由表由裂痕故障块内部树上的节点创建,通过路由表上保留的有用消息决定是否遍历内部树。实验结果证明,随着网格规模的扩大,该算法最大可减少70％的平均路由长度,并且其实现简单,可以有效地延长网络寿命。     

节点间有转向限制的网络最优路径算法

研究含有禁止转向限制的网络中,任意节点间最优路径问题。在Floyd算法基础上,通过引入正向和反向两种路径标记 p_ij、q_ij,建立了一种禁行路径的判断规则,给出了一种适用的路径寻优迭代算法。在不改变网络的拓扑结构的情况下,该算法可同时获得所有任意两点间的最优路径。     

Effective Utilization of Hypercubes in the Presence of Faults

To effectively utilize a faulty hypercube, it is often necessary to reconfigure the hypercube in such a way as to retain as many fault-free nodes as possible. This inspires us to identify maximalincomplete subcubesin a faulty hypercube, as the subcube so reconfigured is often much larger than any complete subcube obtainable and is likely to retain performance better. An efficient algorithm is first presented to find incomplete subcubes in a faulty hypercube. Three applications are then implemented on both an incomplete system and a complete one to measure their actual performance differences. Each application is mapped onto incomplete hypercubes, following the techniques developed for complete hypercubes (possibly with some modifications). Among the three applications,Gaussian eliminationtakes exactly the same mapping scheme on an incomplete system as on a complete one, whileFFTrequires some efforts to adapt it to the incomplete topology. The measured results of the three applications indicate that reconfiguring a faulty hypercube into an incomplete subcube is beneficial in practice.     

Routing in modular fault-tolerant multiprocessor systems

In this paper, we consider a class of modular multiprocessor architectures in which spares are added to each module to cover for faulty nodes within that module, thus forming a fault-tolerant basic block (FTBB). In contrast to reconfiguration techniques that preserve the physical adjacency between active nodes in the system, our goal is to preserve the logical adjacency between active nodes by means of a routing algorithm which delivers messages successfully to their destinations. We introduce two-phase routing strategies that route messages first to their destination FTBB, and then to the destination nodes within the destination FTBB. Such a strategy may be applied to a variety of architectures including binary hypercubes and three-dimensional tori. In the presence of f faults in hypercubes and tori, we show that the worst case length of the message route is min {σ+f, (K+1)σ}+c where σ is the shortest path in the absence of faults, K is the number of spare nodes in an FTBB, and c is a small constant. The average routing overhead is much lower than the worst case overhead