The -Diagnosability for Regular Networks

Lin, Limei; Zhou, Shuming; Hsieh, Sun-Yuan

doi:10.1109/tc.2015.2512866

Cited by 38 publications

(4 citation statements)

References 42 publications

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“…We include the results of diagnosability of the GCPNs in Table 1. It will be challenging and interesting to consider other types of diagnosability for it, such as conditional diagnosability [3], g-good neighbor conditional diagnosability [30], t/kdiagnosability [31] and so on.…”

Section: Discussionmentioning

confidence: 99%

The Diagnosability of the Generalized Cartesian Product of Networks

Chen

Lin

2023

Mathematics

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Motivated by two typical ways to construct multiprocessor systems, matching composition networks and cycle composition networks, we generalize the definition of the Cartesian product of networks and consider the classical diagnosability of the generalized Cartesian product of networks (GCPNs). In this paper, we determine the accurate value of the classical diagnosability of the generalized Cartesian product of networks (GCPNs) under the PMC model and the MM* model.

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Section: Discussionmentioning

confidence: 99%

The Diagnosability of the Generalized Cartesian Product of Networks

Chen

Lin

2023

Mathematics

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“…The t/k-diagnosability of several networks under the PMC model has been determined, including hypercubes [2], star graphs [2,5], mesh-based systems [2], and bijective connection (BC) networks [6,7]. Recently, by utilizing the properties of the 0-test subgraph under the PMC model, Lin et al [8] studied the t/k-diagnosability of regular graphs under the PMC model.…”

Section: Introductionmentioning

confidence: 99%

t/k-Diagnosability of Regular Networks under the Comparison Model

Liang,

Xiao,

Lin

et al. 2024

Sensors

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As multiprocessor systems continue to grow in processor scale, the incidence of faults also increases. As a result, fault diagnosis is becoming a key mechanism for maintaining the normal operation of multiprocessor systems. To explore more effective diagnostic methods, Somani et al. introduced a generalized pessimistic diagnostic strategy, named t/k-diagnosis, in which all faulty nodes are isolated in a set of nodes and at most k fault-free nodes are misdiagnosed, provided that the quantity of faults is limited by t. By imposing certain conditions or restrictions, the t/k-diagnosability of some regular networks under the Preparata, Metze, and Chien (PMC) model has been determined. However, the t/k-diagnosability of many networks under the comparison model remains unidentified. In this paper, we provide new insights into the study of t/k-diagnosability under the comparison model. After introducing some new notions, such as the 0-test unit, 0-test set and 0-test subgraph, under the comparison model, we study the relationship in a system G between the 0-test subgraphs and the components of G−F, where F is the set of faulty nodes, and we obtain some important correlation properties. Based on these results, we study t/k-diagnosability under the comparison model. As a result, the t/k-diagnosability of some regular interconnection networks can be efficiently determined.

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“…In 2018, under the PMC model, Lin et al [16] proposed the size of neighbors of a 4-cycle in general regular graphs, which can be applied to build the relationship between conditional diagnosability and extra connectivity. Moreover, Lin et al [22] also applied the size of neighbors of a subset D to propose the t/k-diagnosability for regular graphs, including n-alternating group graph, n-split-star network, l n -hypermesh and (n, l)star graph. Also, Lin et al [19] proposed the size of neighbors of a subgraph B of order q + 1 in the (n, k)-arrangement graph A n,k , which can be applied to the g-good-neighbor conditional diagnosability.…”

Section: Introductionmentioning

confidence: 99%

Minimum Neighborhood of Alternating Group Graphs

2019

Self Cite

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The minimum neighborhood and combinatorial property are two important indicators of fault tolerance of a multiprocessor system. Given a graph G, θ G (q) is the minimum number of vertices adjacent to a set of q vertices of G (1 ≤ q ≤ |V (G)|). It is meant to determine θ G (q), the minimum neighborhood problem (MNP). In this paper, we obtain θ AG n (q) for an independent set with size q in an n-dimensional alternating group graph AG n , a well-known interconnection network for multiprocessor systems. We first propose some combinatorial properties of AG n. Then, we study the MNP for an independent set of two vertices and obtain that θ AG n (2) = 4n − 10. Next, we prove that θ AG n (3) = 6n − 16. Finally, we propose that θ AG n (4) = 8n − 24. INDEX TERMS Minimum neighborhood, combinatorial property, fault tolerance, independent set, alternating group graphs.

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The -Diagnosability for Regular Networks

Cited by 38 publications

References 42 publications

The Diagnosability of the Generalized Cartesian Product of Networks

The Diagnosability of the Generalized Cartesian Product of Networks

t/k-Diagnosability of Regular Networks under the Comparison Model

Minimum Neighborhood of Alternating Group Graphs

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