scholarly journals The Component Diagnosability of General Networks

2021 ◽  
pp. 1-23
Author(s):  
Hongbin Zhuang ◽  
Wenzhong Guo ◽  
Xiaoyan Li ◽  
Ximeng Liu ◽  
Cheng-Kuan Lin
Keyword(s):  
Fault Diagnosis ◽  
Negative Impact ◽  
Rapid Expansion ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Star Graphs ◽  
Comparison Results ◽  
Text Model ◽  
Text Component ◽  
General Networks

The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly prominent. The [Formula: see text]-component diagnosability of [Formula: see text], denoted by [Formula: see text], is the maximum number of nodes of the faulty set [Formula: see text] that is correctly identified in a system, and the number of components in [Formula: see text] is at least [Formula: see text]. In this paper, we determine the [Formula: see text]-component diagnosability of general networks under the PMC model and MM[Formula: see text] model. As applications, the component diagnosability is explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, hierarchical hypercubes, Cayley graphs generated by transposition trees (except star graphs), and DQcube as well. Furthermore, we provide some comparison results between the component diagnosability and other fault diagnosabilities.

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 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.

Optimal adaptive fault diagnosis for simple multiprocessor systems

Networks ◽  
1999 ◽  
Vol 34 (3) ◽  
pp. 206-214 ◽  
Author(s):  
Evangelos Kranakis ◽  
Andrzej Pelc ◽  
Anthony Spatharis
Keyword(s):  
Fault Diagnosis ◽  
Multiprocessor Systems

Adaptive Diagnosis of Hamiltonian Networks under the Comparison Model

2021 ◽  
pp. 2150015
Author(s):  
Wenjun Liu ◽  
Wenjun Li
Keyword(s):  
Fault Diagnosis ◽  
Upper Bound ◽  
Multiprocessor Systems ◽  
Major Goal ◽  
Comparison Model ◽  
A Value ◽  
Pmc Model ◽  
Diagnosis Algorithm ◽  
Test Outcomes

Adaptive diagnosis is an approach in which tests can be scheduled dynamically during the diagnosis process based on the previous test outcomes. Naturally, reducing the number of test rounds as well as the total number of tests is a major goal of an efficient adaptive diagnosis algorithm. The adaptive diagnosis of multiprocessor systems under the PMC model has been widely investigated, while adaptive diagnosis using comparison model has been independently discussed only for three networks, including hypercube, torus, and completely connected networks. In addition, adaptive diagnosis of general Hamiltonian networks is more meaningful than that of special graph. In this paper, the problem of adaptive fault diagnosis in Hamiltonian networks under the comparison model is explored. First, we propose an adaptive diagnostic scheme which takes five to six test rounds. Second, we derive a dynamic upper bound of the number of fault nodes instead of setting a value like normal. Finally, we present an algorithm such that at least one sequence obtained from cycle partition can be picked out and all nodes in this sequence can be identified based on the previous upper bound.

Diagnosability of Bubble-Sort Star Graphs with Missing Edges

2019 ◽  
Vol 19 (02) ◽  
pp. 1950002 ◽  
Author(s):  
SHIYING WANG ◽  
YINGYING WANG
Keyword(s):  
Multiprocessor System ◽  
Star Graph ◽  
Star Graphs ◽  
Comparison Model ◽  
Model Following ◽  
Strong Property

The diagnosability of a multiprocessor system plays an important role. The bubble-sort star graph BSn has many good properties. In this paper, we study the diagnosis on BSn under the comparison model. Following the concept of the local diagnosability, the strong local diagnosability property is discussed. This property describes the equivalence of the local diagnosability of a node and its degree. We prove that BSn (n ≥ 5) has this property, and it keeps this strong property even if there exist (2n − 5) missing edges in it, and the result is optimal with respect to the number of missing edges.

Relationship Between Extra Connectivity And Component Connectivity In Networks

2020 ◽  
Author(s):  
Xiaoyan Li ◽  
Cheng-Kuan Lin ◽  
Jianxi Fan ◽  
Xiaohua Jia ◽  
Baolei Cheng ◽  
...  
Keyword(s):  
Cayley Graphs ◽  
Multiprocessor System ◽  
Minimum Number ◽  
The Relationship ◽  
General Networks

Abstract Connectivity is a classic measure for reliability of a multiprocessor system in the case of processor failures. Extra connectivity and component connectivity are two important indicators of the reliability of a multiprocessor system in presence of failing processors. The $h$-extra connectivity $\kappa _{h}(G)$ of a graph $G$ is the minimum number of nodes whose removal will disconnect $G$, and every remaining component has at least $h+1$ nodes. Moreover, the $h$-component connectivity $c\kappa _{h}(G)$ of $G$ is the minimum number of nodes whose deletion results in a graph with at least $h$ components. However, the extra connectivity and component connectivity of many well-known networks have been independently investigated. In this paper, we determine the relationship between extra connectivity and component connectivity of general networks. As applications, the extra connectivity and component connectivity are explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, Cayley graphs generated by transposition trees and hierarchical hypercubes as well.

scholarly journals First assessment of habitat suitability and connectivity for the golden jackal in north-eastern Italy

2020 ◽  
Vol 100 (6) ◽  
pp. 631-643
Author(s):  
Elisa Torretta ◽  
Olivia Dondina ◽  
Claudio Delfoco ◽  
Luca Riboldi ◽  
Valerio Orioli ◽  
...  
Keyword(s):  
Habitat Selection ◽  
Habitat Suitability ◽  
Negative Impact ◽  
Rapid Expansion ◽  
Golden Jackal ◽  
Landscape Resistance ◽  
Least Cost Path ◽  
Study Region ◽  
North Eastern ◽  
Kernel Approach

AbstractCompared with the rapid expansion across Europe, the golden jackal colonization of Italy is still limited and slow. No study focused on the habitat selection or landscape connectivity for this species was performed in Italy; thus, the potential distribution and dispersal patterns in the country remain unknown. Our objectives were to evaluate the suitability of the Friuli-Venezia Giulia region (north-eastern Italy) for the golden jackal, as well as to identify the ecological corridors connecting the areas currently occupied by the species. Corridors modelling allowed us both to hypothesize the dispersal dynamics occurring in the study region and to identify possible obstacles to future range expansion. We surveyed golden jackal presence in two study areas, covering an area of 500 km2, from March 2017 to February 2018. Using collected data, we modelled the species home-range scale habitat suitability based on an ensemble modelling approach. Subsequently, a habitat suitability prediction at a finer scale was used to estimate landscape resistance, starting from which, we modelled dispersal corridors among areas currently occupied by the species using a factorial least cost path and a cumulative resistant kernel approach. Our results indicated a moderate potential for large parts of the study region to support the occurrence of golden jackal family groups, whose presence seems to be mainly driven by the presence of wide areas covered by broadleaved forests and shrublands and by the absence of wide intensive agricultural areas. The predicted connectivity networks showed that three main permeable corridors are likely to connect golden jackal occurrence areas within the study region, while all the other corridors are characterized by a very low path density. Both the habitat selection and connectivity analyses showed a strong negative impact of the intensive cultivated plain on species stable presence and movement providing critical information for the conservation of the golden jackal in Italy.

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 .

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