On deriving conditional diagnosability of interconnection networks

Cheng, Eddie; Lipták, László; Qiu, Ke; Shen, Zhizhang

doi:10.1016/j.ipl.2012.06.008

Cited by 45 publications

(11 citation statements)

References 10 publications

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“…To the best of out knowledge, there is no existing work on this topic. It is motivated by the conditional diagnosability of some graphs [3,4,30,34,37,40]. Zhou et al [34,37] have proposed the conditional diagnosability of hierarchical hypercubes and crossed cubes under the comparison model, respectively.…”

Section: Motivations and Goalsmentioning

confidence: 99%

“…Xu et al [30] investigated the conditional diagnosability of shuffle-cube under the PMC model, while they did not consider the conditional diagnosability under the comparison model. Cheng et al [3,4] gave a unified approach to explore the conditional diagnosability of a class of interconnection networks, but it does not contain the shuffle-cube. Zhu et al [40] determined the relationship among diagnosability, strong diagnosability and conditional diagnosability of strong networks.…”

Section: Motivations and Goalsmentioning

confidence: 99%

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Conditional diagnosability and strong diagnosability of shuffle-cubes under the comparison model

Lin

Zhou

2014

International Journal of Computer Mathematics

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The growing size of multiprocessor systems increases the vulnerability to component failures. It is crucial to locate and replace faulty processors to maintain the system's high reliability. Processor fault diagnosis is essential to the reliability of a multiprocessor system and the diagnosabilities of many well-known networks (such as hierarchical hypercubes and crossed cubes [S. Zhou, L. Lin and J.-M. Xu, Conditional fault diagnosis of hierarchical hypercubes, Int. J. Comput. Math. 89(16) (2012), pp. 2152-2164 and S. Zhou, The conditional diagnosability of crossed cubes under the comparison model, Int. J. Comput. Math. 87 (15) (2010), pp. 3387-3396]) have been investigated in the literature. A system is t-diagnosable if all faulty nodes can be identified without replacement when the number of faults does not exceed t, where t is some positive integer. Furthermore, a system is strongly t-diagnosable if it is t-diagnosable and can achieve (t + 1)-diagnosability except for the case where a node's neighbours are all faulty. In addition, conditional diagnosability has been widely accepted as a new measure of diagnosability by assuming that any fault-set cannot contain all neighbours of any node in a multiprocessor system. In this paper, we determine the conditional diagnosability and strong diagnosability of an n-dimensional shuffle-cube SQ n , a variant of hypercube for multiprocessor systems, under the comparison model. We show that the conditional diagnosability of shuffle-cube SQ n (n = 4k + 2 and k ≥ 2) is 3n − 9, and SQ n is strongly n-diagnosable under the comparison model.

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Section: Motivations and Goalsmentioning

confidence: 99%

Section: Motivations and Goalsmentioning

confidence: 99%

Conditional diagnosability and strong diagnosability of shuffle-cubes under the comparison model

Lin

Zhou

2014

International Journal of Computer Mathematics

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“…Based on this assumption, Lai et al [2005] introduced the concept of conditional diagnosability and showed that the conditional diagnosability of an ndimensional hypercube Q n is 4n − 7 for n ≥ 5 under the PMC model. Several studies also contributed to the conditional diagnosability of multiprocessor systems under both the PMC and MM* models, including hypercubes [Hsu et al 2009;Lai et al 2005], star graphs [Chang and Hsieh 2014;Cheng et al 2012;Lin et al 2008], k-ary n-cubes Hsieh and Kao 2013], Bijective Connection (BC) networks Xu et al 2009;Zhu 2008], Cayley graphs (only in the MM* model) [Lin et al 2008], and folded hypercubes (PMC) . In this article, we evaluate the conditional diagnosability for n under the PMC model and show it is 4n − 11 for n ≥ 4.…”

Section: Introductionmentioning

confidence: 99%

Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees under the PMC Model

Chang

Cheng

Hsieh

2015

ACM Trans. Des. Autom. Electron. Syst.

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Processor fault diagnosis has played an essential role in measuring the reliability of a multiprocessor system. The diagnosability of many well-known multiprocessor systems has been widely investigated. Conditional diagnosability is a novel measure of diagnosability by adding a further condition that any fault set cannot contain all the neighbors of every node in the system. Several known structural properties of Cayley graphs are exhibited. Based on these properties, we investigate the conditional diagnosability of Cayley graphs generated by transposition trees under the PMC model and show that it is 4n − 11 for n ≥ 4 except for the n-dimensional star graph for which it has been shown to be 8n−21 for n ≥ 5 (refer to Chang and Hsieh [2014]).

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“…Others evaluated the conditional diagnosability of multiprocessor systems under both the PMC and MM* models, including hypercubes [22], [27], k-ary n-cubes [5], [21], Bijective Connection (BC) networks [23], [40], [49], Cayley graphs (only in the MM* model) [32], and folded hypercubes (PMC) [50]. Cheng et al [6] and Lin et al [32] have shown that the conditional diagnosability of S n is 3n À 7 for n ! 4 under the MM* model.…”

Section: Introductionmentioning

confidence: 99%

Structural Properties and Conditional Diagnosability of Star Graphs by Using the PMC Model

Chang

Hsieh

2014

IEEE Trans. Parallel Distrib. Syst.

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Processor fault diagnosis has played an important role in measuring the reliability of a multiprocessor system; the diagnosability of many well-known multiprocessor systems has been widely investigated. Conditional diagnosability is a novel measure of diagnosability. It includes a condition whereby any fault set cannot contain all the neighbors of any node in a system. In this paper, the conditional diagnosability of star graphs by using the PMC model is evaluated. Several new structural properties of star graphs are derived. Based on these properties, the conditional diagnosability of an n-dimensional star graph is determined to be 8n À 21 for n ! 5.

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On deriving conditional diagnosability of interconnection networks

Cited by 45 publications

References 10 publications

Conditional diagnosability and strong diagnosability of shuffle-cubes under the comparison model

Conditional diagnosability and strong diagnosability of shuffle-cubes under the comparison model

Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees under the PMC Model

Structural Properties and Conditional Diagnosability of Star Graphs by Using the PMC Model

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