Cluster-Composition Graphs: t/t-Diagnosabilty and its Application

2013 ◽  
Vol 411-414 ◽  
pp. 2115-2118
Author(s):  
Jheng Cheng Chen ◽  
Chang Hsiung Tsai
Keyword(s):  
Multiprocessor Systems ◽  
Connected Component ◽  
Unified Approach ◽  
Star Graphs ◽  
Pmc Model ◽  
Cluster Composition ◽  
Composition Graph

In this paper, we propose a unified approach for computing the t/t-diagnosability of numerous multiprocessor systems under the PMC model, including hypercube-like graphs, star graphs, and pancake graphs. Our approach first defines a superclass of graphs, called j-order cluster-composition graphs, to cover them.We then show that the 1-order simple cluster-composition graph is t/t-diagnosable if it contains no connected component with size less than 2t+1, where t is the minimal number of neighbors of any pair of vertices of the graph. Based on this result, the t/t-diagnosability of the above multiprocessor systems can be computed efficiently.

Adaptive Diagnosis of Hamiltonian Networks under the Comparison Model

2021 ◽  
pp. 2150015
Author(s):  
Wenjun Liu ◽  
Wenjun Li
Keyword(s):  
Fault Diagnosis ◽  
Upper Bound ◽  
Multiprocessor Systems ◽  
Major Goal ◽  
Comparison Model ◽  
A Value ◽  
Pmc Model ◽  
Diagnosis Algorithm ◽  
Test Outcomes

Adaptive diagnosis is an approach in which tests can be scheduled dynamically during the diagnosis process based on the previous test outcomes. Naturally, reducing the number of test rounds as well as the total number of tests is a major goal of an efficient adaptive diagnosis algorithm. The adaptive diagnosis of multiprocessor systems under the PMC model has been widely investigated, while adaptive diagnosis using comparison model has been independently discussed only for three networks, including hypercube, torus, and completely connected networks. In addition, adaptive diagnosis of general Hamiltonian networks is more meaningful than that of special graph. In this paper, the problem of adaptive fault diagnosis in Hamiltonian networks under the comparison model is explored. First, we propose an adaptive diagnostic scheme which takes five to six test rounds. Second, we derive a dynamic upper bound of the number of fault nodes instead of setting a value like normal. Finally, we present an algorithm such that at least one sequence obtained from cycle partition can be picked out and all nodes in this sequence can be identified based on the previous upper bound.

A Note on the Nature Diagnosability of Alternating Group Graphs Under the PMC Model and MM* Model

2018 ◽  
Vol 18 (01) ◽  
pp. 1850005 ◽  
Author(s):  
SHIYING WANG ◽  
LINGQI ZHAO
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Alternating Group ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Free Node ◽  
Pmc Model ◽  
Important Study ◽  
Communication Links ◽  
Alternating Group Graph

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No faulty set can contain all the neighbors of any fault-free node in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we prove the following. (1) The nature diagnosability of AGn is 4n − 10 for n − 5 under the PMC model and MM* model. (2) The nature diagnosability of the 4-dimensional alternating group graph AG4 under the PMC model is 5. (3) The nature diagnosability of AG4 under the MM* model is 4.

Fault Tolerance on Star Graphs

1997 ◽  
Vol 08 (02) ◽  
pp. 127-142 ◽  
Author(s):  
Shuo-Cheng Hu ◽  
Chang-Biau Yang
Keyword(s):  
Fault Tolerance ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Constant Time ◽  
Multiprocessor Systems ◽  
Star Graph ◽  
Cycle Structure ◽  
Star Graphs ◽  
Broadcasting Algorithm

The capability of fault tolerance is one of the advantages of multiprocessor systems. In this paper, we prove that the fault tolerance of an n-star graph is 2n-5 with restriction to the forbidden faulty set. And we propose an algorithm for examining the connectivity of an n-star graph when there exist at most 2n - 4 faults. The algorithm requires O(n2 log n) time. Besides, we improve the fault-tolerant routing algorithm proposed by Bagherzadeh et al. by calculating the cycle structure of a permutation and the avoidance of routing message to a node without any nonfaulty neighbor. This calculation needs only constant time. And then, we propose an efficient fault-tolerant broadcasting algorithm. When there is no fault, our broadcasting algorithm remains optimal. The penalty is O(n) if there exists only one fault, and the penalty is O(n2) if there exist at most n - 2 faults.

Persistence of Hybrid Diagnosability of Regular Networks Under Testing Diagnostic Model

2020 ◽  
Author(s):  
Guanqin Lian ◽  
Shuming Zhou ◽  
Eddie Cheng ◽  
Jiafei Liu ◽  
Gaolin Chen
Keyword(s):  
Fault Tolerance ◽  
Assignment Problem ◽  
Diagnostic Model ◽  
Multiprocessor Systems ◽  
Node Failure ◽  
Pmc Model ◽  
Free Network ◽  
Delta G ◽  
Regular Networks ◽  
Fault Diagnosability

Abstract Diagnosability is an important metric to fault tolerance and reliability for multiprocessor systems. However, plenty of research on fault diagnosability focuses on node failure. In practical scenario, not only node failures take place but also link malfunctions may arise. In this work, we investigate the diagnosability of general regular networks with failing nodes as well as missing malfunctional links. Let $S$ be a set of the missing links and broken-down nodes. We first prove that the diagnosability of the survival graph $G\setminus S$ persists $\delta (G\setminus S)$ under the PMC model (Preparata, F.P., Metze, G. and Chien, R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Trans. Electron. Comput., EC-16, 848–854) for a $t$-regular and $t$-connected triangle-free network $G$ subject to $|S|\leq t-1$ and $|V(G)|\geq 3t-2$ ($t\geq 3$). Furthermore, we determine the diagnosability of $G\setminus S$ for some kinds of extensively explored $t$-regular networks with triangles subject to $|S|\leq t-1$ ($t\geq 3$).

scholarly journals Two-Round Diagnosability Measures for Multiprocessor Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jiarong Liang ◽  
Qian Zhang ◽  
Changzhen Li
Keyword(s):  
Fault Diagnosis ◽  
Time Complexity ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Pmc Model ◽  
Diagnosis Algorithm ◽  
Conditional Diagnosability ◽  
Novel Concept ◽  
Measure Index

In a multiprocessor system, as a key measure index for evaluating its reliability, diagnosability has attracted lots of attentions. Traditional diagnosability and conditional diagnosability have already been widely discussed. However, the existing diagnosability measures are not sufficiently comprehensive to address a large number of faulty nodes in a system. This article introduces a novel concept of diagnosability, called two-round diagnosability, which means that all faulty nodes can be identified by at most a one-round replacement (repairing the faulty nodes). The characterization of two-round t-diagnosable systems is provided; moreover, several important properties are also presented. Based on the abovementioned theories, for the n-dimensional hypercube Qn, we show that its two-round diagnosability is n2+n/2, which is n+1/2 times its classic diagnosability. Furthermore, a fault diagnosis algorithm is proposed to identify each node in the system under the PMC model. For Qn, we prove that the proposed algorithm is the time complexity of On2n.

scholarly journals The Component Diagnosability of General Networks

2021 ◽  
pp. 1-23
Author(s):  
Hongbin Zhuang ◽  
Wenzhong Guo ◽  
Xiaoyan Li ◽  
Ximeng Liu ◽  
Cheng-Kuan Lin
Keyword(s):  
Fault Diagnosis ◽  
Negative Impact ◽  
Rapid Expansion ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Star Graphs ◽  
Comparison Results ◽  
Text Model ◽  
Text Component ◽  
General Networks

The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly prominent. The [Formula: see text]-component diagnosability of [Formula: see text], denoted by [Formula: see text], is the maximum number of nodes of the faulty set [Formula: see text] that is correctly identified in a system, and the number of components in [Formula: see text] is at least [Formula: see text]. In this paper, we determine the [Formula: see text]-component diagnosability of general networks under the PMC model and MM[Formula: see text] model. As applications, the component diagnosability is explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, hierarchical hypercubes, Cayley graphs generated by transposition trees (except star graphs), and DQcube as well. Furthermore, we provide some comparison results between the component diagnosability and other fault diagnosabilities.

A Linear Time Pessimistic Diagnosis Algorithm for Hypermesh Multiprocessor Systems under the PMC Model

2014 ◽  
Vol 63 (12) ◽  
pp. 2894-2904
Author(s):  
Hong-Chun Hsu ◽  
Kuang-Shyr Wu ◽  
Cheng-Kuan Lin ◽  
Chiou-Yng Lee ◽  
Chien-Ping Chang
Keyword(s):  
Linear Time ◽  
Multiprocessor Systems ◽  
Pmc Model ◽  
Diagnosis Algorithm
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