&lt;inline-formula&gt; 
                     &lt;tex-math notation="LaTeX"&gt;$t/t$ &lt;/tex-math&gt;
                  &lt;/inline-formula&gt;-Diagnosability and &lt;inline-formula&gt; 
                     &lt;tex-math notation="LaTeX"&gt;$t/k$ &lt;/tex-math&gt;
                  &lt;/inline-formula&gt;-Diagnosability for Augmented Cube Networks

Fault diagnosis of processors plays a critical role in assessing the reliability of multiprocessor systems. The interconnection network’s diagnosability is an important metric for measuring its self-diagnostic capability which has been extensively studied in many novel mutiprocessor systems. Permanent fault diagnosability for many mutiprocessor systems has been determined; however intermittent fault diagnosability is hard to obtain due to its crypticity. In this paper, we focus on the problem pertaining to the diagnosability in the intermittent fault situation. First, by learning the characteristics of intermittent fault diagnosis in PMC model, we propose some theorems and lemmas for intermittent fault diagnosability. Secondly, we give the range of intermittent fault diagnosability of product network. Lastly, by adopting the theorems, we propose an Auto-IFD algorithm to find the intermittent faults of the hypercube network and conduct experiments to verify the theorems.

show abstract

Many-to-Many Disjoint Paths in Augmented Cubes With Exponential Fault Edges

Zhang

2021

IEEE Access

View full text Add to dashboard Cite

It is common knowledge that edge disjoint paths have close relationship with the edge connectivity. Motivated by the well-known Menger theorem, we find that the maximum cardinality of edge disjoint paths connecting any two disjoint connected subgraphs with g vertices in G can also define by the minimum modified edge-cut, called the g-extra edge-connectivity of G (λ g (G)). It is the cardinality of the minimum set of edges in G, if such a set exists, whose deletion disconnects G and leaves every remaining component with at least g vertices. The n-dimensional augmented cube AQ n is a variant of hypercube Q n . In this paper, we observe that the g-extra edge-connectivity of the augmented cube for some exponentially large enough g exists a concentration behavior, for about 72.22 percent values of g ≤ 2 n−1 , and that the g-extra edge-connectivity of AQ n (n ≥ 3) concentrates on n 2 − 1 special values. Specifically, we prove that the exact value of g-extra edge-connectivity of augmented cube is a constant 2( n 2 − r)2+r , where n ≥ 3, r = 1, 2, . . . , n 2 − 1 and l r = 2 2r+1 −2 3 if n is odd and l r = 2 2r+2 −4 3 if n is even. The above upper and lower bounds of g are sharp. Moreover, we also obtain the exponential edge disjoint paths in AQ n with edge faults.INDEX TERMS Fault tolerance, many-to-many edge disjoint paths, interconnected networks, exponential fault edges.

show abstract

<inline-formula> <tex-math notation="LaTeX">$t/t$ </tex-math> </inline-formula>-Diagnosability and <inline-formula> <tex-math notation="LaTeX">$t/k$ </tex-math> </inline-formula>-Diagnosability for Augmented Cube Networks

Cited by 5 publications

References 36 publications

t/t-Diagnosability of BCube Network

t/t-Diagnosability of BCube Network

Intermittent Fault Diagnosis Of Product Network Based On PMC Model

Many-to-Many Disjoint Paths in Augmented Cubes With Exponential Fault Edges

Contact Info

Product

Resources

About