Reliability Evaluation of Generalized Exchanged Hypercubes Based on Imprecise Diagnosis Strategies

2021 ◽  
Vol 31 (01) ◽  
pp. 2150005
Author(s):  
Hongbin Zhuang ◽  
Sunjian Zheng ◽  
Ximeng Liu ◽  
Cheng-Kuan Lin ◽  
Xiaoyan Li
Keyword(s):  
Interconnection Networks ◽  
Maximum Degree ◽  
Essential Role ◽  
Wiener Index ◽  
Reliability Evaluation ◽  
Diagnostic Analysis ◽  
Pmc Model ◽  
Text Model ◽  
Diagnosis Algorithm ◽  
Fault Diagnostic

Fault diagnostic analysis is extremely important for interconnection networks. The [Formula: see text]-diagnosis imprecise strategy plays an essential role in the reliability of networks. The [Formula: see text]-diagnosis strategy can detect up to [Formula: see text] faulty vertices which might include at most [Formula: see text] misdiagnosed vertices. The exchanged hypercube is obtained by systematically removing links from a binary hypercube, which has smaller maximum degree and Wiener index than the hypercube. We use [Formula: see text] to denote the generalized exchanged hypercube, and show in this paper that [Formula: see text] is [Formula: see text]-diagnosable with [Formula: see text] and [Formula: see text] under the PMC model and MM[Formula: see text] model. We also propose a [Formula: see text]-diagnosis algorithm on [Formula: see text]. As a side benefit, the [Formula: see text]-diagnosability of the dual-cube-like network [Formula: see text] can be directly obtained from our results.

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 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].

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.

Semi-Deterministic Construction of Scale-Free Networks with Designated Parameters

2018 ◽  
Vol 18 (01) ◽  
pp. 1850001
Author(s):  
NAOKI TAKEUCHI ◽  
SATOSHI FUJITA
Keyword(s):  
Degree Distribution ◽  
Interconnection Networks ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Scale Free ◽  
Scale Free Networks ◽  
Ideal Number ◽  
Message Propagation ◽  
Deterministic Construction ◽  
The Ideal

Scale-free networks have several favorable properties as the topology of interconnection networks such as the short diameter and the quick message propagation. In this paper, we propose a method to construct scale-free networks in a semi-deterministic manner. The proposed algorithm extends the Bulut's algorithm for constructing scale-free networks with designated minimum degree k and maximum degree m, in such a way that: (1) it determines the ideal number of edges derived from the ideal degree distribution; and (2) after connecting each new node to k existing nodes as in the Bulut’s algorithm, it adjusts the number of edges to the ideal value by conducting add/removal of edges. We prove that such an adjustment is always possible if the number of nodes in the network exceeds [Formula: see text]. The performance of the algorithm is experimentally evaluated.

Extremal trees with respect to the Steiner Wiener index

2019 ◽  
Vol 11 (06) ◽  
pp. 1950067
Author(s):  
Jie Zhang ◽  
Guang-Jun Zhang ◽  
Hua Wang ◽  
Xiao-Dong Zhang
Keyword(s):  
Maximum Degree ◽  
Computational Analysis ◽  
Degree Sequence ◽  
Wiener Index ◽  
Extremal Problems ◽  
Difficult Problem ◽  
Computational Results ◽  
Number Of Leaves ◽  
Extremal Structure ◽  
Chemical Trees

The well-known Wiener index is defined as the sum of pairwise distances between vertices. Extremal problems with respect to it have been extensively studied for trees. A generalization of the Wiener index, called the Steiner Wiener index, takes the sum of minimum sizes of subgraphs that span [Formula: see text] given vertices over all possible choices of the [Formula: see text] vertices. We consider the extremal problems with respect to the Steiner Wiener index among trees of a given degree sequence. First, it is pointed out minimizing the Steiner Wiener index in general may be a difficult problem, although the extremal structure may very likely be the same as that for the regular Wiener index. We then consider the upper bound of the general Steiner Wiener index among trees of a given degree sequence and study the corresponding extremal trees. With these findings, some further discussion and computational analysis are presented for chemical trees. We also propose a conjecture based on the computational results. In addition, we identify the extremal trees that maximize the Steiner Wiener index among trees with a given maximum degree or number of leaves.

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.

Analysis on the Component Connectivity of Enhanced Hypercubes

2020 ◽  
Author(s):  
Liqiong Xu ◽  
Litao Guo
Keyword(s):  
Connected Graph ◽  
Interconnection Networks ◽  
Unsolved Problem ◽  
Reliability Evaluation ◽  
Minimum Number ◽  
Appl Math

Abstract Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The component connectivity is an important parameter for the reliability evaluation of interconnection networks and is a generalization of the traditional connectivity. The $g$-component connectivity $c\kappa _g (G)$ of a non-complete connected graph $G$ is the minimum number of vertices whose deletion results in a graph with at least $g$ components. Determining the $g$-component connectivity is still an unsolved problem in many interconnection networks. Let $Q_{n,k}$ ($1\leq k\leq n-1$) denote the $(n, k)$-enhanced hypercube. In this paper, let $n\geq 7$ and $1\leq k \leq n-5$, we determine $c\kappa _{g}(Q_{n,k}) = g(n + 1) - \frac{1}{2}g(g + 1) + 1$ for $2 \leq g \leq n$. The previous result in Zhao and Yang (2019, Conditional connectivity of folded hypercubes. Discret. Appl. Math., 257, 388–392) is extended.

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 .

Sign in / Sign up

Export Citation Format

Share Document