The 2-good-neighbor diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM⁎ model

Discrete Applied Mathematics

2017

Self Cite

Connectivity plays an important role in measuring the fault tolerance of interconnection networks. The g-good-neighbor connectivity of an interconnection network G is the minimum cardinality of g-good-neighbor cuts. Diagnosability of a multiprocessor system is one important study topic. A new 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 bubblesort star graph BS n has many good properties. In this paper, we prove that 2-good-neighbor connectivity of BS n is 8n − 22 for n ≥ 5 and the 2-good-neighbor connectivity of BS 4 is 8; the 2-good-neighbor diagnosability of BS n is 8n − 19 under the PMC model and MM * model for n ≥ 5.

Section: Introductionmentioning

confidence: 99%

The 2-good-neighbor connectivity and 2-good-neighbor diagnosability of bubble-sort star graph networks

Discrete Applied Mathematics

2017

Self Cite

“…In Ref. 21, Wang et al studied the nature diagnosability of CΓ n under the PMC model and MM* model and proved that the nature diagnosability of the system is less than or equal to the conditional diagnosability of the system. Therefore, the nature diagnosability of the system is nature and one important study topic.…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

2018

J. Inter. Net.

Self Cite

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 AG 4 under the PMC model is 5. (3) The nature diagnosability of AG 4 under the MM * model is 4. system G is said to be t-diagnosable if all faulty processors can be identified without replacement, provided that the number of presented faults does not exceed t. The diagnosability t(G) of G is the maximum value of t such that G is t-diagnosable. 4,5,13 For a t-diagnosable system, Dahbura and Masson 4 proposed an algorithm with time complex O(n 2.5 ), which can effectively identify the set of faulty processors.Several diagnosis models were proposed to identify the faulty processors. One major approach is the Preparata, Metze, and Chien's (PMC) diagnosis model introduced by Preparata et al. 17 The diagnosis of the system is achieved through two linked processors testing each other. Another major approach is the Maeng and Malek's (MM) diagnosis model, namely the comparison diagnosis model, proposed by Maeng and Malek. 15 In the MM model, to diagnose a system, a node sends the same task to two of its neighbors, and then compares their responses. In the event of a random node failure, it is very unlikely that all the neighbors of any node fail simultaneously in the system. This reason has motivated research on the restricted diagnosability of the system. In 2005, Lai et al. 13 introduced the restricted diagnosability of the system called the conditional diagnosability. They considered the situation that no faulty set can contain all the neighbors of any node in the system. Since the probability that all the neighbors of a fault node fail and create faults is more to the probability that all the neighbors of a fault-free node fail and create faults in the system, we consider the situation that 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. In 2012, Peng et al. 16 proposed a measure for fault diagnosis of systems, namely, the g-good-neighbor diagnosability (which is also called the g-goodneighbor conditional diagnosability), which requires that every fault-free node has at least g fault-free neighbors. In Ref. 16, they studied the g-good-neighbor diagnosability of the n-dimensional hypercube under the PMC model. In 2016, Wang and Han 20 studied the g-...

“…In [7], Wang and Han studied the g-good-neighbor diagnosability of the n-dimensional hypercube under the MM* model. There is a significant amount of research on the g-good-neighbor diagnosability of graphs [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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

Ren

2018

Information

Self Cite

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.