LINEARLY MANY FAULTS IN (n, k)-STAR GRAPHS

Yuan, Allen; Cheng, Eddie; Lipták, László

doi:10.1142/s0129054111008994

Cited by 38 publications

(15 citation statements)

References 17 publications

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“…In both cases, c + 1 is proved to be tight by following the process as summarized in Theorem 4.1. The following result is recently proved in [10] for the (n, k)-star graph.…”

Section: Lemma 41 Let G Be a Graph Such That For Any T ⊂ V |T | Cmentioning

confidence: 92%

On deriving conditional diagnosability of interconnection networks

Cheng

Lipták

Qiu

et al. 2012

Information Processing Letters

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“…In both cases, c + 1 is proved to be tight by following the process as summarized in Theorem 4.1. The following result is recently proved in [10] for the (n, k)-star graph.…”

Section: Lemma 41 Let G Be a Graph Such That For Any T ⊂ V |T | Cmentioning

confidence: 92%

On deriving conditional diagnosability of interconnection networks

Cheng

Lipták

Qiu

et al. 2012

Information Processing Letters

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“…Cheng and Lipták [5] extended the results on S n with linearly many faults. Yuan et al [32] generalized the results on (n, k)-star graphs. Cheng et al [7] Downloaded by [University of Tasmania] at 12:05 13 October 2014 presented a similar result for the two-tree-generated networks with linearly many faults.…”

Section: Fault Tolerance Of the Hhcmentioning

confidence: 95%

Conditional fault diagnosis of hierarchical hypercubes

Zhou

Lin

2012

International Journal of Computer Mathematics

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The design of large dependable multiprocessor systems requires quick and precise mechanisms for detecting the faulty nodes. The system-level fault diagnosis is the process of identifying faulty processors in a system through testing. This paper shows that the largest connected component of the survival graph contains almost all remaining vertices in the hierarchical hypercube HHC n when the number of faulty vertices is up to two or three times of the traditional connectivity. Based on this fault resiliency, we establish that the conditional diagnosability of HHC n (n = 2 m + m, m ≥ 2) under the comparison model is 3m − 2, which is about three times of the traditional diagnosability.

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“…Also, Yang et al [31] proved that, in an n-star graph network S n with a subset D ⊆ V (S n ) of size |D| ≤ 2n − 4, the size of big component without D is at least |V (S n )| − |D| − 2. Moreover, Cheng and Lipták [11] computed the size of big component in cayley graphs generated by transpositions trees when deleting linearly many faults, and Yuan and Cheng [32] further proposed the size of big component in (n, k)-star graphs when deleting linearly many faults. Zhang et al in [34] proposed an efficient disk-based directed graph processing by using the component structure.…”

Section: Introductionmentioning

confidence: 99%

Component Reliability Evaluation on Split-Stars

2019

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The failure of some key vertices in a network, due to either attacks or malfunctioning, may break the network into several disconnected components-the vertices within each component are connected, but there are no connections between components. When this happens, two measures should be of concern:(1) the number of components in the remaining network; and (2) the size of each component. When a given number of ''break vertices'' are removed from a network, we hope to have as few components as possible in the remaining network. On the other hand, it is certainly desirable that the components are as large as possible. Therefore both the number of components and the size of the maximal component after removing certain vertices can be a metric of a network's fault tolerability, an important dimension of its robustness. In this paper, we examine the split-star, denoted S 2 n , in terms of this metric. We prove that when an arbitrary subset of vertices D with |D| ≤ 6n−15 is removed from S 2 n , the remaining network will have at most 3 components, with the largest component having at least n! − |D| − 3 vertices. With |D| ≤ 8n − 21, the remaining network has at most 4 components, with the largest component's size at least n!−|D|−5. As a theoretical application, the r-component connectivity of S 2 n is estimated by using the obtained maximal component and the minimal neighbor-set of independent set of size r. Moreover, we present a bound of r-component edge connectivity on S 2 n by considering the minimal neighbor edge-set of appropriate substructures in S 2 n .

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LINEARLY MANY FAULTS IN (n, k)-STAR GRAPHS

Cited by 38 publications

References 17 publications

On deriving conditional diagnosability of interconnection networks

On deriving conditional diagnosability of interconnection networks

Conditional fault diagnosis of hierarchical hypercubes

Component Reliability Evaluation on Split-Stars

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