Number Of Faulty Links Research Articles

Hybrid fault diagnosis capability analysis of regular graphs under the PMC model

Diagnosabilty is an important metric to the capability of fault identification for multiprocessor systems. However, most researches on diagnosability focus on vertex fault. In real circumstances, not only vertex faults take place but also malfunctions may arise. In this paper, we study the diagnosability of k-regular 2-cn graph with missing edges. Let be a set of missing edges in graph G with . We prove that the diagnosability of is at most for . Furthermore, we obtain that the worst-case diagnosability (h-edge tolerable diagnosability), denoted by , is maximum number of faulty nodes that a system G can guarantee to locate when the number of faulty links does not exceed h. As applications, the diagnosabilities of many networks with missing edges are determined under the PMC model.

Hybrid fault diagnosis capability analysis of triangle-free graphs

Fault diagnosis capability is an important metric of the reliability of multiprocessor systems. The h-edge tolerable diagnosability is the maximum number of faulty nodes that the system can guarantee to locate when the number of faulty links does not exceed h. In fact, the 0-edge tolerable diagnosability is exactly the traditional diagnosability. In this paper, we determine the h-edge tolerable diagnosabilities of triangle-free graphs under the PMC model and the MM⁎ model, respectively, which extend the results of triangle-free regular graphs (Wei and Xu (2019) [26]). As applications, the h-edge tolerable diagnosabilities of many networks are determined under the PMC model and the MM⁎ model.

Hybrid fault diagnosis capability analysis of regular graphs

Fault diagnosis of systems is an important area of study in the design and maintenance of multiprocessor systems. A new measure for fault diagnosis of systems, namely, h-edge tolerable diagnosability, is the maximum number of faulty nodes that a system G can guarantee to locate when the number of faulty links does not exceed h, denoted by the(G). Particularly, t0e(G) is the traditional diagnosability of G. Chang et al. (2005) [5] determined the traditional diagnosabilities of regular graphs. In this paper, we establish the h-edge tolerable diagnosabilities of regular graphs under the PMC model and the MM⁎ model, which extends their results and provides a more precise characterization for the fault diagnosis capability of regular graphs. As applications, the h-edge tolerable diagnosabilities of many networks are determined under the PMC model and the MM⁎ model.

A combinatorial study of substar reliability of the star network

Hierarchical networks may be divided into subnetworks having the same topological properties of the original network. The star graph, an example of hierarchical networks, has been studied extensively as a viable candidate for massively parallel systems. For a given number of faulty links and using a combinatorial approach, lower bounds on probability of having one or more (n − 1)-stars in an n-star are determined. An identification algorithm is presented to find an available (n − 1)-star in an n-star containing a set of faulty links.

Fault Immunization Concept for Self-Organizing Mapping Neural Networks

Self-Organizing Mapping (SOM) neural network has been widely used in pattern classification, vector quantization, and image compression. We consider the problem of strengthening the reliability of a SOM neural network by the technique of fault immunization of the synaptic links of each neuron which is similar to the concept of biological immunization. Instead of assuming the stuck-at-0 and stuck-at-1 as in those studies, we consider a general case of stuck-at-a, where a is a real value. The only assumption that we consider is only one neuron can be faulty at any time. No restriction on the number of faulty links of the neuron. Let wi,j be the weight of synaptic link j of neuron i obtained after the winner-take-all classification. Weight wi,j is immunized by adding a constant ∊i,j, either positive or negative, to wi,j. A neuron reaches its maximum fault immunization if the value of wi,j + ∊i,j can be either increased or decreased as much as possible without creating any misclassification. Thus, the fault immunization problem is formulated as an optimization problem on finding the value of each ∊i,j. A technique to find the value of wi,j + ∊i,j is proposed and its application to enhance the transmission reliability in image compression area is introduced.

FAULT IMMUNIZATION CONCEPT FOR SELF-ORGANIZING MAPPING NEURAL NETWORKS

Self-Organizing Mapping (SOM) neural network has been widely used in pattern classification, vector quantization, and image compression. We consider the problem of strengthening the reliability of a SOM neural network by the technique of fault immunization of the synaptic links of each neuron which is similar to the concept of biological immunization. Instead of assuming the stuck-at-0 and stuck-at-1 as in those studies, we consider a general case of stuck-at-a, where a is a real value. The only assumption that we consider is only one neuron can be faulty at any time. No restriction on the number of faulty links of the neuron. Let wi,j be the weight of synaptic link j of neuron i obtained after the winner-take-all classification. Weight wi,j is immunized by adding a constant ∊i,j, either positive or negative, to wi,j. A neuron reaches its maximum fault immunization if the value of wi,j + ∊i,j can be either increased or decreased as much as possible without creating any misclassification. Thus, the fault immunization problem is formulated as an optimization problem on finding the value of each ∊i,j. A technique to find the value of wi,j + ∊i,j is proposed and its application to enhance the transmission reliability in image compression area is introduced.

Distributed fault-tolerant ring embedding and reconfiguration in hypercubes

To embed a ring in a hypercube is to find a Hamiltonian cycle through every node of the hypercube. It is obvious that no 2/sup n/-node Hamiltonian cycle exists in an n-dimensional faulty hypercube which has at least one faulty node. However, if a hypercube has faulty links only and the number of faulty links is at most n-2, at least one 2/sup n/-node Hamiltonian cycle can be found. In this paper, we propose a distributed ring-embedding algorithm that can find a Hamiltonian cycle in a fault-free or faulty n-dimensional hypercube (Q,), and the complexity is O(n) parallel steps. The algorithm is based on the recursion property of the hypercube and the free-link dimension concept. In some cases, even when the number of faulty links is larger than n-2, Hamiltonian cycles may still exist. We show that the largest possible number of faulty links that can be tolerated is 2/sup n-1/-1. The performance and the constraints of the fault-tolerant algorithm is also analyzed in detail in this paper. Furthermore, a dynamic reconfiguration algorithm for an embedded ring is proposed and discussed. Due to the distributed nature of the algorithms, they are useful for the simulation of ring-based multiprocessors on MIMD hypercube multiprocessors.

Broadcasting in synchronous networks with dynamic faults

The problem of broadcasting in a network is to disseminate information from one node to all other nodes by transmitting it over communication links that connect nodes. We consider the time of broadcasting in the presence of at most k dynamic link failures. If a node knows source information, then in the next step all its neighbors connected by operational links also get to know it. Faults are dynamic, in the sense that a link may alternate arbitrarily between being operational or faulty, provided that, at every time step, the number of faulty links does not exceed k. The time bounds on broadcasting are considered with respect to two parameters: the number k of faulty links and the diameter d of the underlying graph. Broadcasting is guaranteed to be successful if and only if the edge connectivity of the network exceeds k, and we consider only such networks. For a fixed k, it is shown that broadcasting is always completed in time O(dk+1), where the bound is a function of diameter d. For a fixed d, it is shown that broadcasting is always completed in time O(kd/2–1), where the bound is a function of k. We prove that these orders of magnitude cannot be improved in general. Among networks, particularly interesting are those in which broadcasting time is close to their diameter in the presence of at most k dynamic faults, where k + 1 is the edge-connectivity of the network. We show that multidimensional tori have this property. © 1996 John Wiley & Sons, Inc.

A depth-first search routing algorithm for star graphs and its performance evaluation

A fault-tolerant routing algorithm has been developed for star graph interconnection topology by using a depth-first search strategy. The proposed algorithm routes a message from the source to the destination along an optimal path with a very high probability and is guaranteed to trace a path as long as the source and the destination are not disconnected. We derive exact mathematical expressions for the probabilities that the algorithm will compute an optimal path for a given number of faulty links in the network. The analysis reveals many interesting topological properties of the star graphs.

SOME RESULTS ON BUDS, STEMS AND FAULT TOLERANCE IN HYPERCUBES OF DIMENSION ⋚ 5

Abstract We determine the minimum number of faulty links in a 5-dimensional hypercube so that no 2-dimensional subcube is fault free. The degree sequences of some related extremal graphs are also determined.