Conditional fault diagnosis of hierarchical hypercubes

Zhou, Shuming; Lin, Limei; Xu, Jie

doi:10.1080/00207160.2012.710325

Cited by 17 publications

(5 citation statements)

References 32 publications

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“…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. 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.…”

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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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%

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

Lin

Zhou

2014

International Journal of Computer Mathematics

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“…Thus they are more refined measures of reliability for multiprocessor systems. The restricted connectivity, super connectivity and extra connectivity of many interconnection networks have been explored [2], [3], [4], [5], [10], [11], [29], [37], [44], [51], [15], [38], [39], [40], [31], [44], [28], [41], [42], [27], [33], [35], [19], [30], [32], [50], [51], [26], [48], [23], [44], [46], [24], [9], [49], [45], [47].…”

Section: Introductionmentioning

confidence: 99%

From Graph Isoperimetric Inequality to Network Connectivity -- A New Approach

Zhu¹,

Ma²,

Guo³

et al. 2016

Preprint

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We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's connectivity is the minimum number of nodes, whose removal will cause the network disconnected. It is a basic and important measure for the network's reliability, hence its overall robustness. Several conditional connectivities have been proposed in the past for the purpose of accurately reflecting various realistic network situations, with extra connectivity being one such conditional connectivity. In this paper, we will use isoperimetric properties of the hypercube network to obtain its extra connectivity. The result of the paper for the first time establishes a relationship between the age-old isoperimetric problem and network connectivity.

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“…In addition, hypercubes are very popular as seed for complex network topologies such as those for hierarchical interconnection networks (HINs) (eg. hierarchical hypercubes [3], [4], [5], [6], hierarchical cubic networks [7], [8], [9], metacubes [10], [11], dual-cubes [12], [13], etc).…”

Section: Introductionmentioning

confidence: 99%

On Hypercube Routing and Fault Tolerance with Bit Constraint

Bossard

Kaneko

2014

2014 Second International Symposium on Computing and Networking

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Due to their simplicity, hypercubes are very popular as interconnection networks of parallel systems. While several routing algorithms have been described for this network topology in the literature, we consider in this paper hypercube routing with an additional restriction: bit constraint. Simply speaking, routing will be conducted amongst a particular subset of nodes, all of which must satisfy a condition regarding their bit weights (a.k.a. Hamming weights). Such kind of routing restriction has several applications including simplification of disjoint paths routing and hypercube embedded network routing. In this paper, we describe two hypercube routing algorithms satisfying such restriction, the first one for shortest-path routing and the second one for faulttolerant point-to-point routing. Correctness and complexities of the proposed algorithms are formally proved. The shortest-path routing algorithm described is shown to be time-optimal. Lastly, an empirical evaluation of the proposed algorithm is conducted in order to inspect its practical behaviour.

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Conditional fault diagnosis of hierarchical hypercubes

Cited by 17 publications

References 32 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

From Graph Isoperimetric Inequality to Network Connectivity -- A New Approach

On Hypercube Routing and Fault Tolerance with Bit Constraint

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