A kind of conditional fault tolerance of -star graphs

Yang, Weihua; Li, Hengzhe; Guo, Xiaofeng

doi:10.1016/j.ipl.2010.08.015

Cited by 36 publications

(6 citation statements)

References 18 publications

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“…Remark 1. Among the regular interconnection networks, there are many famous networks that are triangle-free, for example, hypercube-like networks [18], star networks [7], and the exchanged hypercube network [24].…”

Section: Preliminariesmentioning

confidence: 99%

“…Whenever a faulty node is identified by the system, it should be repaired or replaced with an additional one. The process of identifying faulty processors is referred to as fault diagnosis, which has been widely studied in [1][2][3][4][5][6][7][8][9]. The diagnosability, a key measurement of self-diagnosis capacity, of a system is the upper limit on the number of faulty processors that a system is certain to identify.…”

Section: Introductionmentioning

confidence: 99%

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The Strong Local Diagnosability of a Hypercube Network with Missing Edges

2018

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In the research on the reliability of a connection network, diagnosability is an important problem that should be considered. In this article, a new concept regarding diagnosability, called strong local diagnosability (SLD), which describes the local status of the strong diagnosability (SD) of a system, is presented. In addition, a few important results related to the SLD of a node of a system are presented. Based on these results, we conclude that in a hypercube network of n dimensions, denoted by Q n , the SLD of a node is equal to its degree when n ⩾ 4. Moreover, we explore the SLD of a node of an incomplete hypercube network. We determine that the SLD of a node is equal to its remaining degree (RD) in an incomplete hypercube network, which is true provided that the number of faulty edges in this hypercube network does not exceed n − 3 . Finally, we discuss the SLD of a node for an incomplete hypercube network and obtain the following results: if the minimum RD of nodes in an incomplete hypercube network of n-dimensions is greater than 3, then the SLD of any node is still equal to its RD provided that the number of faulty edges does not exceed 7 n − 3 − 1. If the RD of each node is greater than 4, then the SLD of each node is also equal to its RD, no matter how many faulty edges exist in Q n .

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Strong Local Diagnosability of a Hypercube Network with Missing Edges

2018

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“…for the star graph S n , Wan, Zhang [21] determined κ 2 (S n ) = 6(n − 3) for n ≥ 4; for the (n, k)-star graphs S n,k , Yang et al [29] proved that κ 2 (S n,k ) = n + 2k − 5 for 2 ≤ k ≤ n − 2; Zhang et al [30] proved κ 2 (AG n ) = 6n − 18 for n ≥ 5.…”

Section: Introductionmentioning

confidence: 99%

“…The super connectivity of some graphs determined by several authors. For example, for the hypercube Q n , the twisted cube T Q n , the cross cube CQ n , the Möbius cube MQ n and the locally twisted cube LT Q n , Xu et al [26] showed that their super connectivity and the super edge-connectivity are all 2n − 2; for the star graph S n , Hu and Yang [17] proved that κ 1 (S n ) = 2n − 4 for n ≥ 3; for the augmented cube AQ n , Ma, Liu and Xu [19,20] determined κ 1 (AQ n ) = 4n − 8 for n ≥ 6 and λ 1 (AQ n ) = 4n − 4 for n ≥ 2; for the (n, k)star graphs S n,k , Yang et al [29] proved that κ 1 (S n,k ) = n + k − 3; for the n-dimensional alternating group graph AG n , Cheng et al [5] determined κ 1 (AG n ) = 4n − 11 for n ≥ 5.…”

Section: Introductionmentioning

confidence: 99%

Fault-tolerant analysis of augmented cubes

Ma¹,

Song²,

Xu³

2012

Preprint

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The augmented cube AQ n , proposed by Choudum and Sunitha [S. A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71-84], is a (2n − 1)-regular (2n − 1)-connected graph (n ≥ 4). This paper determines that the 2-extra connectivity of AQ n is 6n − 17 for n ≥ 9 and the 2-extra edge-connectivity is 6n − 9 for n ≥ 4. That is, for n ≥ 9 (respectively, n ≥ 4), at least 6n−17 vertices (respectively, 6n − 9 edges) of AQ n have to be removed to get a disconnected graph that contains no isolated vertices and isolated edges. When the augmented cube is used to model the topological structure of a large-scale parallel processing system, these results can provide more accurate measurements for reliability and fault tolerance of the system.

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“…For a system having at most t faulty nodes, if it can determine a set with the size s (s ≤ t) that contains all its faulty nodes, then it is t/s-diagnosable. Numerous studies have been reported on a t/s-diagnosable system, such as [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Two-Round Diagnosability Measures for Multiprocessor Systems

Liang

Zhang

2020

Complexity

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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.

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A kind of conditional fault tolerance of -star graphs

Cited by 36 publications

References 18 publications

The Strong Local Diagnosability of a Hypercube Network with Missing Edges

The Strong Local Diagnosability of a Hypercube Network with Missing Edges

Fault-tolerant analysis of augmented cubes

Two-Round Diagnosability Measures for Multiprocessor Systems

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