Extraconnectivity of hypercubes

Yang, Weihua; Meng, Jixiang

doi:10.1016/j.aml.2008.07.016

Cited by 112 publications

(27 citation statements)

References 5 publications

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“…Motivated by the research on the extra connectivity of some networks, including hypercubes, BC networks, hypercube-like networks, alternating group graphs, and split-star networks [2], [4], [21], [25], [31], [32], [40], we establish the g-extra connectivity for the (n, k)-arrangement graph A n,k , and show that the A n,k 's one-extra connectivity is…”

Section: Introductionmentioning

confidence: 99%

The Extra Connectivity, Extra Conditional Diagnosability, and <inline-formula> <tex-math notation="LaTeX"> $t/m$</tex-math> </inline-formula>-Diagnosability of Arrangement Graphs

Zhou

Hsieh

2016

IEEE Trans. Rel.

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Extra connectivity is an important indicator of the robustness of a multiprocessor system in presence of failing processors. The g-extra conditional diagnosability and the t/mdiagnosability are two important diagnostic strategies at systemlevel that can significantly enhance the system's self-diagnosing capability. The g-extra conditional diagnosability is defined under the assumption that every component of the system removing a set of faulty vertices has more than g vertices. The t/mdiagnosis strategy can detect up to t faulty processors which might include at most m misdiagnosed processors, where m is typically a small integer number. In this paper, we analyze the combinatorial properties and fault tolerant ability for an (n, k)-arrangement graph, denoted by A n,k , a well-known interconnection network proposed for multiprocessor systems. We first establish that the A n,k 's one-extra connectivity is (2k − 1) 3 (k ≥ 4, n ≥ k + 2), and three-extra connectivity is (4k − 4)(n − k) − 4 ( k ≥ 4, n ≥ k + 2 or k ≥ 3, n ≥ k + 3), respectively. And then, we address the g-extra conditional diagnosability of A n,k under the PMC model for 1 ≤ g ≤ 3. Finally, we determine that the (n, k)-arrangement graph A n,k is [(2k − 1)(n − k) − 1]/1-diagnosable (k ≥ 4, n ≥ k + 2), [(3k − 2)(n − k) − 3]/2-diagnosable (k ≥ 4, n ≥ k + 2), and [(4k − 4)(n − k) − 4]/3-diagnosable (k ≥ 4, n ≥ k + 3) under the PMC model, respectively.

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Section: Introductionmentioning

confidence: 99%

The Extra Connectivity, Extra Conditional Diagnosability, and <inline-formula> <tex-math notation="LaTeX"> $t/m$</tex-math> </inline-formula>-Diagnosability of Arrangement Graphs

Zhou

Hsieh

2016

IEEE Trans. Rel.

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“…Recently, Yang and Meng [27] determined the extra connectivity of hypercubes, Hsu et al [12] went further to establish the component connectivity of hypercubes. Yang et al [31], Cheng and Lipman [2] and Cheng and Lipták [3] evaluated the size of surviving graph S n − F of star graph S n , where F is a subset of V (S n ) with |F| ≤ 2n − 4.…”

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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“…So BC networks have received a great deal of attention and research in the past [17], [19], [20], [21], [22]. Recently, Yang and Meng [10] connectivity of n-dimensional (n ! 4) hypercubes for 1 h n. In this paper, By exploring the boundary problem of BC networks, we have determined the h-extra connectivity of an n-dimensional BC network X n for 0 h n À 4: h ðX n Þ ¼ nðh þ 1Þ À 1 2 hðh þ 3Þ.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the study of extra connectivity is of great significance in exploring the reliability of interconnection networks. The extra connectivity of many interconnection networks has been determined in the past [10], [11], [12], [13].…”

Section: Introductionmentioning

confidence: 99%

Reliability Evaluation of BC Networks

Zhu

Wang

Cheng

2013

IEEE Trans. Comput.

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Reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems. Extra connectivity determination and faulty networks' structure analysis are two important aspects for the reliability evaluation of interconnection networks. An n-dimensional bijective connection network (in brief, BC network), denoted by X n , is an n-regular graph with 2 n vertices and n2 nÀ1 edges. The hypercubes, M€ obius cubes, crossed cubes, and twisted cubes are some examples of the BC networks. By exploring the boundary problem of the BC networks, we prove that when n ! 4 and 0 h n À 4 the h-extra connectivity of an n-dimensional BC network X n is h ðX n Þ ¼ nðh þ 1Þ À 1 2 hðh þ 3Þ. Furthermore, there exists a large connected component and the remaining small components have at most h vertices in total if the total number of faulty vertices is strictly less its h-extra connectivity. As an application, the results on the h-extra connectivity and structure of faulty networks on hypercubes, M€ obius cubes, crossed cubes, and twisted cubes are obtained.

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Extraconnectivity of hypercubes

Cited by 112 publications

References 5 publications

The Extra Connectivity, Extra Conditional Diagnosability, and <inline-formula> <tex-math notation="LaTeX"> $t/m$</tex-math> </inline-formula>-Diagnosability of Arrangement Graphs

The Extra Connectivity, Extra Conditional Diagnosability, and <inline-formula> <tex-math notation="LaTeX"> $t/m$</tex-math> </inline-formula>-Diagnosability of Arrangement Graphs

Conditional fault diagnosis of hierarchical hypercubes

Reliability Evaluation of BC Networks

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