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 .

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.

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.

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].

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.

scholarly journals Two-Round Diagnosability Measures for Multiprocessor Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jiarong Liang ◽  
Qian Zhang ◽  
Changzhen Li
Keyword(s):  
Fault Diagnosis ◽  
Time Complexity ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Pmc Model ◽  
Diagnosis Algorithm ◽  
Conditional Diagnosability ◽  
Novel Concept ◽  
Measure Index

In a multiprocessor system, as a key measure index for evaluating its reliability, diagnosability has attracted lots of attentions. Traditional diagnosability and conditional diagnosability have already been widely discussed. However, the existing diagnosability measures are not sufficiently comprehensive to address a large number of faulty nodes in a system. This article introduces a novel concept of diagnosability, called two-round diagnosability, which means that all faulty nodes can be identified by at most a one-round replacement (repairing the faulty nodes). The characterization of two-round t-diagnosable systems is provided; moreover, several important properties are also presented. Based on the abovementioned theories, for the n-dimensional hypercube Qn, we show that its two-round diagnosability is n2+n/2, which is n+1/2 times its classic diagnosability. Furthermore, a fault diagnosis algorithm is proposed to identify each node in the system under the PMC model. For Qn, we prove that the proposed algorithm is the time complexity of On2n.

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.

Reliability of DQcube Based on g-Extra Conditional Fault

2020 ◽  
Author(s):  
Hong Zhang ◽  
Jixiang Meng
Keyword(s):  
Fault Diagnosis ◽  
Interconnection Networks ◽  
Pmc Model ◽  
Minimum Number ◽  
Conditional Diagnosability

Abstract Diagnosability and connectivity are important metrics for the reliability and fault diagnosis capability of interconnection networks, respectively. The g-extra connectivity of a graph G, denoted by $\kappa _g(G)$, is the minimum number of vertices whose deletion will disconnect the network and every remaining component has more than $g$ vertices. The g-extra conditional diagnosability of graph G, denoted by $t_g(G)$, is the maximum number of faulty vertices that the graph G can guarantee to identify under the condition that every fault-free component contains at least g+1 vertices. In this paper, we first determine that g-extra connectivity of DQcube is $\kappa _g(G)=(g+1)(n+1)-\frac{g(g+3)}{2}$ for $0\leq g\leq n-3$ and then show that the g-extra conditional diagnosability of DQcube under the PMC model $(n\geq 4, 1\leq g\leq n-3)$ and the MM$^\ast$ model $(n\geq 7, 1\leq g\leq \frac{n-3}{4})$ is $t_g(G)=(g+1)(n+1)-\frac{g(g+3)}{2}+g$, respectively.

Diagnosability and Diagnostic Algorithm for Pancake Graph under the Comparison Model

2015 ◽  
Vol 15 (01n02) ◽  
pp. 1550005
Author(s):  
WENJUN LIU ◽  
CHENG-KUAN LIN
Keyword(s):  
Fault Diagnosis ◽  
Interconnection Networks ◽  
Linear Time ◽  
Hamiltonian Path ◽  
Diagnostic Algorithm ◽  
Efficient Algorithms ◽  
Comparison Model ◽  
Diagnosis Model

Fault diagnosis is important for the reliability of interconnection networks. This paper addresses the fault diagnosis of n-dimensional pancake graph Pn under the comparison diagnosis model. By the concept of local diagnosability, we first prove that the diagnosabitly of Pn is n − 1, and it has strong local diagnosability property even if there are n − 3 faulty edges. Furthermore, we present efficient algorithms to locate extended star and Hamiltonian path structures in Pn, respectively. According to the works of Li et al. and Lai, the extended star and Hamiltonian path structures can be used to identify all faulty vertices in linear time, provided the number of faulty vertices is no more than n − 1.

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