Finding cycles in hierarchical hypercube networks

The g-good neighbor connectivity κ g (G) and g-good-neighbor diagnosability t g (G) are two important parameters to evaluate the reliability and fault tolerance for an interconnection network G. So far, almost all known results about κ g (G) and t g (G) are about special g except the hypercubes, the star graphs, the k-ary n-cubes, and so on. In this paper, we focus on κ g (HHC n ) and t g (HHC n ) for the n-dimensional hierarchical hypercube networkIn addition, we show that t g (HHC n ) = 2 g (m + 2 − g) − 1 under the PMC model and MM * model for 1 ≤ g ≤ m − 1.

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“…1, where m = 2. There are some results about hierarchical hypercube network, one can refer [8]- [10], [18], [19] etc. for the detail.…”

Section: Preliminariesmentioning

confidence: 99%

Reliability Assessment of Hierarchical Hypercube Networks

Zhao

Hao

2019

IEEE Access

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“…Wu et al [23] gave a construction of node disjoint paths of any two vertices in HHC with the estimation of length on these paths. Wu et al [24] showed that the HHC is bipancyclic. Some fault tolerant problems are still open for HHCs.…”

Section: Hierarchical Hypercubesmentioning

confidence: 99%

“…Lemma 3.1 [18][19][20]23,24] For n = 2 m + m and m ≥ 2, HHC n has the following combinatorial properties:…”

Section: Fault Tolerance Of the Hhcmentioning

confidence: 99%

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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Structure of Fibonacci cubes: a survey

Klavžar

2011

J Comb Optim

107

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Finding cycles in hierarchical hypercube networks

Cited by 7 publications

References 8 publications

Reliability Assessment of Hierarchical Hypercube Networks

Reliability Assessment of Hierarchical Hypercube Networks

Conditional fault diagnosis of hierarchical hypercubes

Structure of Fibonacci cubes: a survey

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