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

Information ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 275 ◽  
Author(s):  
Shiying Wang ◽  
Yunxia Ren
Keyword(s):  
Interconnection Network ◽  
Multiprocessor System ◽  
Important Research ◽  
Free Node ◽  
System A ◽  
Arrangement Graph ◽  
Pmc Model ◽  
Important Research Topic ◽  
Good Neighbor ◽  
Special Case

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.

Diagnosability of the Cayley Graph Generated by Complete Graph with Missing Edges under the MM$^{\ast }$ Model

2019 ◽  
Vol 63 (9) ◽  
pp. 1438-1447
Author(s):  
Yunxia Ren ◽  
Shiying Wang
Keyword(s):  
Fault Diagnosis ◽  
Complete Graph ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Research Topic ◽  
Multiprocessor System ◽  
Important Research ◽  
System A ◽  
Important Research Topic ◽  
Special Case

Abstract Diagnosability of a multiprocessor system is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph. Under the Maeng and Malek's (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 all pairs of its adjacent nodes. In 2009, Chiang and Tan (Using node diagnosability to determine $t$-diagnosability under the comparison diagnosis (cd) model. IEEE Trans. Comput., 58, 251–259) proposed a new viewpoint for fault diagnosis of the system, namely, the node diagnosability. As a new topology structure of interconnection networks, the nest graph $CK_{n}$ has many good properties. In this paper, we study the local diagnosability of $CK_{n}$ and show it has the strong local diagnosability property even if there exist $(\frac{n(n-1)}{2}-2)$ missing edges in it under the MM$^{*}$ model, and the result is optimal with respect to the number of missing edges.

Connectivity and Nature Diagnosability of Leaf-Sort Graphs

2020 ◽  
Vol 20 (03) ◽  
pp. 2050011
Author(s):  
JUTAO ZHAO ◽  
SHIYING WANG
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Research Topic ◽  
Multiprocessor System ◽  
Important Research ◽  
Edge Connectivity ◽  
Topology Structure ◽  
Pmc Model ◽  
Important Research Topic

The connectivity and diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and interconnection network has a underlying topology, which usually presented by a graph. As a famous topology structure of interconnection networks, the n-dimensional leaf-sort graph CFn has many good properties. In this paper, we prove that (a) the restricted edge connectivity of CFn (n ≥ 3) is 3n − 5 for odd n and 3n − 6 for even n; (b) CFn (n ≥ 5) is super restricted edge-connected; (c) the nature diagnosability of CFn (n ≥ 4) under the PMC model is 3n − 4 for odd n and 3n − 5 for even n; (d) the nature diagnosability of CFn (n ≥ 5) under the MM* model is 3n − 4 for odd n and 3n − 5 for even n.

scholarly journals The g-Good-Neighbor Diagnosability of Bubble-Sort Graphs under Preparata, Metze, and Chien’s (PMC) Model and Maeng and Malek’s (MM)* Model

Information ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 21
Author(s):  
Shiying Wang ◽  
Zhenhua Wang
Keyword(s):  
Fault Diagnosis ◽  
Interconnection Networks ◽  
Multiprocessor System ◽  
Topology Structure ◽  
Free Node ◽  
Pmc Model ◽  
Good Neighbor

Diagnosability of a multiprocessor system is an important topic of study. A measure for fault diagnosis of the system restrains that every fault-free node has at least g fault-free neighbor vertices, which is called the g-good-neighbor diagnosability of the system. As a famous topology structure of interconnection networks, the n-dimensional bubble-sort graph B n has many good properties. In this paper, we prove that (1) the 1-good-neighbor diagnosability of B n is 2 n − 3 under Preparata, Metze, and Chien’s (PMC) model for n ≥ 4 and Maeng and Malek’s (MM) ∗ model for n ≥ 5 ; (2) the 2-good-neighbor diagnosability of B n is 4 n − 9 under the PMC model and the MM ∗ model for n ≥ 4 ; (3) the 3-good-neighbor diagnosability of B n is 8 n − 25 under the PMC model and the MM ∗ model for n ≥ 7 .

A Note on the Nature Diagnosability of Alternating Group Graphs Under the PMC Model and MM* Model

2018 ◽  
Vol 18 (01) ◽  
pp. 1850005 ◽  
Author(s):  
SHIYING WANG ◽  
LINGQI ZHAO
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Alternating Group ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Free Node ◽  
Pmc Model ◽  
Important Study ◽  
Communication Links ◽  
Alternating Group Graph

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No faulty set can contain all the neighbors of any fault-free node in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we prove the following. (1) The nature diagnosability of AGn is 4n − 10 for n − 5 under the PMC model and MM* model. (2) The nature diagnosability of the 4-dimensional alternating group graph AG4 under the PMC model is 5. (3) The nature diagnosability of AG4 under the MM* model is 4.

Connectivity and Diagnosability of Leaf-Sort Graphs

2020 ◽  
Vol 30 (03) ◽  
pp. 2040004
Author(s):  
Mujiangshan Wang ◽  
Dong Xiang ◽  
Shiying Wang
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Multiprocessor System ◽  
Important Research ◽  
Research Topics ◽  
Topology Structure ◽  
Pmc Model ◽  
Text Model

The connectivity and diagnosability of a multiprocessor system and an interconnection network are two important research topics. The system and the network have an underlying topology, which is usually presented by a graph. As a topology structure of interconnection networks, the [Formula: see text]-dimensional leaf-sort graph [Formula: see text] has many good properties. In this paper, we prove that (a) [Formula: see text] is tightly [Formula: see text] super connected for odd [Formula: see text] and [Formula: see text], and tightly [Formula: see text] super connected for even [Formula: see text] and [Formula: see text]; (b) under the PMC model and MM[Formula: see text] model, the diagnosability [Formula: see text] for odd [Formula: see text] and [Formula: see text], and [Formula: see text] for even [Formula: see text] and [Formula: see text].

A Note of Independent Number and Domination Number of Qn,k,m-Graph

2019 ◽  
Vol 29 (03) ◽  
pp. 1950011
Author(s):  
Jiafei Liu ◽  
Shuming Zhou ◽  
Zhendong Gu ◽  
Yihong Wang ◽  
Qianru Zhou
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Domination Number ◽  
Multiprocessor System ◽  
Star Graph ◽  
Minimum Cardinality ◽  
Arrangement Graph ◽  
Independent Number ◽  
Potential Applications ◽  
By Products

The independent number and domination number are two essential parameters to assess the resilience of the interconnection network of multiprocessor systems which is usually modeled by a graph. The independent number, denoted by [Formula: see text], of a graph [Formula: see text] is the maximum cardinality of any subset [Formula: see text] such that no two elements in [Formula: see text] are adjacent in [Formula: see text]. The domination number, denoted by [Formula: see text], of a graph [Formula: see text] is the minimum cardinality of any subset [Formula: see text] such that every vertex in [Formula: see text] is either in [Formula: see text] or adjacent to an element of [Formula: see text]. But so far, determining the independent number and domination number of a graph is still an NPC problem. Therefore, it is of utmost importance to determine the number of independent and domination number of some special networks with potential applications in multiprocessor system. In this paper, we firstly resolve the exact values of independent number and upper and lower bound of domination number of the [Formula: see text]-graph, a common generalization of various popular interconnection networks. Besides, as by-products, we derive the independent number and domination number of [Formula: see text]-star graph [Formula: see text], [Formula: see text]-arrangement graph [Formula: see text], as well as three special graphs.

scholarly journals The r-Extra Diagnosability of Hyper Petersen Graphs

2021 ◽  
pp. 1-12
Author(s):  
Shiying Wang
Keyword(s):  
Fault Tolerance ◽  
Fault Diagnosis ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Petersen Graph ◽  
Multiprocessor System ◽  
Topology Structure ◽  
Pmc Model ◽  
Petersen Graphs ◽  
Text Model

The diagnosability of a multiprocessor system or an interconnection network plays an important role in measuring the fault tolerance of the network. In 2016, Zhang et al. proposed a new measure for fault diagnosis of the system, namely, the [Formula: see text]-extra diagnosability, which restrains that every fault-free component has at least [Formula: see text] fault-free nodes. As a famous topology structure of interconnection networks, the hyper Petersen graph [Formula: see text] has many good properties. It is difficult to prove the [Formula: see text]-extra diagnosability of an interconnection network. In this paper, we show that the [Formula: see text]-extra diagnosability of [Formula: see text] is [Formula: see text] for [Formula: see text] and [Formula: see text] in the PMC model and for [Formula: see text] and [Formula: see text] in the MM[Formula: see text] model.

scholarly journals An All-Batch Loss for Constructing Prediction Intervals

2021 ◽  
Vol 11 (4) ◽  
pp. 1728
Author(s):  
Hua Zhong ◽  
Li Xu
Keyword(s):  
Gradient Descent ◽  
State Of The Art ◽  
Prediction Interval ◽  
Feedforward Neural Networks ◽  
Important Research ◽  
Likelihood Principle ◽  
High Quality ◽  
Construction Methods ◽  
Important Research Topic ◽  
Benchmark Datasets

The prediction interval (PI) is an important research topic in reliability analyses and decision support systems. Data size and computation costs are two of the issues which may hamper the construction of PIs. This paper proposes an all-batch (AB) loss function for constructing high quality PIs. Taking the full advantage of the likelihood principle, the proposed loss makes it possible to train PI generation models using the gradient descent (GD) method for both small and large batches of samples. With the structure of dual feedforward neural networks (FNNs), a high-quality PI generation framework is introduced, which can be adapted to a variety of problems including regression analysis. Numerical experiments were conducted on the benchmark datasets; the results show that higher-quality PIs were achieved using the proposed scheme. Its reliability and stability were also verified in comparison with various state-of-the-art PI construction methods.

A Bibliometric Review on Outcome-Based Learning for Graduate Employability: Mapping the Research Front

2021 ◽  
pp. 002205742110164
Author(s):  
Mohammad Zahir Raihan ◽  
Md. Abul Kalam Azad
Keyword(s):  
Research Trend ◽  
Future Research ◽  
Research Front ◽  
Important Research ◽  
R Software ◽  
Future Research Agenda ◽  
Graduate Employability ◽  
Important Research Topic ◽  
Bibliometric Review ◽  
First Time

The outcome-based learning for graduate employability in higher education has been an important research topic among the policymakers, academicians, and researchers over the years. Yet, no bibliometric review on this topic has been published. This study, for the first time, examines bibliometric analysis on this topic examining current research trend and future research agenda. The bibliometrix package in R software and VOSviewer software are used for visualization and interpretation of results. A content analysis is performed to manually examine the bibliometric results.

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