Conditional diagnosability of arrangement graphs under the PMC model

Lin, Limei; Zhou, Shuming; Wang, Dajin

doi:10.1016/j.tcs.2014.06.041

Cited by 34 publications

(9 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…. Fault tolerant routing and conditional diagnosability of arrangement graphs have been widely investigated [5], [6], [8], [22]- [24], [38], [39].…”

Section: Arrangement Graphs a Nkmentioning

confidence: 99%

“…In this section, we will establish the {1, 2, 3}-extra connectivities of arrangement graphs by some obtained fault tolerant properties [24], [39].…”

Section: Extra Connectivity Of a Nkmentioning

confidence: 99%

“…Lemma 6 ( [24]): Let F be a vertex cut of A n,k (k ≥ 3, n ≥ k + 2) such that |F | ≤ (4k − 4)(n − k) − 5. Then, A n,k − F satisfies one of the following conditions.…”

Section: Extra Connectivity Of a Nkmentioning

confidence: 99%

See 2 more Smart Citations

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.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…. Fault tolerant routing and conditional diagnosability of arrangement graphs have been widely investigated [5], [6], [8], [22]- [24], [38], [39].…”

Section: Arrangement Graphs a Nkmentioning

confidence: 99%

“…In this section, we will establish the {1, 2, 3}-extra connectivities of arrangement graphs by some obtained fault tolerant properties [24], [39].…”

Section: Extra Connectivity Of a Nkmentioning

confidence: 99%

See 1 more Smart Citation

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.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In 2005, Lai et al [19] introduced a restricted diagnosability of the system called conditional diagnosability by assuming that it is impossible that all neighbors of one vertex are faulty simultaneously. The diagnosabilities and conditional diagnosabilities of many networks are studied in literatures [1]- [3], [11]- [14], [15], [17]- [18], [21], [22], [28], [37] etc. Inspired by this concept, Peng et al [25] then proposed the g-good-neighbor diagnosability, which requires every fault-free vertex has at least g fault-free neighbors.…”

Section: Introductionmentioning

confidence: 99%

Fault diagnosability of data center networks

Hao

Zhou

2019

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

The data center networks D n,k , proposed in 2008, has many desirable features such as high network capacity. A kind of generalization of diagnosability for network G is g-goodneighbor diagnosability which is denoted by t g (G). Let κ g (G) be the R g -connectivity. Lin et. al. in [IEEE Trans. on Reliability, 65 (3) (2016) 1248-1262] and Xu et. al in [Theor. Comput. Sci. 659 (2017) 53-63] gave the same problem independently that: the relationship between the R g -connectivity κ g (G) and t g (G) of a general graph G need to be studied in the future. In this paper, this open problem is solved for general regular graphs. We firstly establish the relationship of κ g (G) and t g (G), and obtain that t g (G) = κ g (G) + g under some conditions. Secondly, we obtain the g-good-neighbor diagnosability of D k,n which are t g (D k,n ) = (g + 1)(k − 1) + n + g for 1 ≤ g ≤ n − 1 under the PMC model and the MM model, respectively. Further more, we show that D k,n is tightly super (n + k − 1)-connected for n ≥ 2 and k ≥ 2 and we also prove that the largest connected component of the survival graph contains almost all of the remaining vertices in D k,n when 2k +n−2 vertices removed.

show abstract

“…The arrangement graph A n,k is more flexible than the star graph in selecting the major design parameters: the number, degree, and diameter of the vertex. At the same time, most of the nice properties of the star graph are preserved (for details, see [26][27][28][29][30][31][32]). In this paper, we show (1) ((g + 1)(k − 2) + 2 − (g+1) 2 2 )(n − k) + g + 1 ≤ t g (A n,k ) ≤ [(g + 1)(k − 1) + 1](n − k) under the PMC model and MM* model for n ≥ 4, k ∈ [3, n − 2], g ∈ [3, n − k);…”

Section: Introductionmentioning

confidence: 99%

g-Good-Neighbor Diagnosability of Arrangement Graphs under the PMC Model and MM* Model

Wang

Ren

2018

Information

View full text Add to dashboard Cite

Diagnosability of a multiprocessor system is an important research topic. The system and interconnection network has a underlying topology, which usually presented by a graph G = (V, E). In 2012, a measurement for fault tolerance of the graph was proposed by Peng et al. This measurement is called the g-good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. Under the PMC model, to diagnose the system, two adjacent nodes in G are can perform tests on each other. Under the MM model, to diagnose the system, a node sends the same task to two of its neighbors, and then compares their responses. The MM* is a special case of the MM model and each node must test its any pair of adjacent nodes of the system. As a famous topology structure, the (n, k)-arrangement graph A n,k , has many good properties. In this paper, we give the g-good-neighbor diagnosability of A n,k under the PMC model and MM* model.

show abstract

Conditional diagnosability of arrangement graphs under the PMC model

Cited by 34 publications

References 26 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

Fault diagnosability of data center networks

g-Good-Neighbor Diagnosability of Arrangement Graphs under the PMC Model and MM* Model

Contact Info

Product

Resources

About