Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees under the PMC Model

Discrete Applied Mathematics

2017

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

“…vertices. CΓ n as a interconnection network model received much attention, see [3][4][5][6][7]10,12,14,19,20,22] for the details.…”

Section: The Cayley Graph Generated By the Transposition Treementioning

confidence: 99%

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

Lin

Theoretical Computer Science

2016

Diagnosability is an important metric for measuring the reliability of multiprocessor systems.In 2012, Peng et al. proposed a new measure for fault diagnosis of the system, which is called ggood-neighbor diagnosability that restrains every fault-free node containing at least g fault-free neighbors. As a favorable topology structure of interconnection networks, the Cayley graph CΓ n generated by the transposition tree Γ n has many good properties. In this paper, we give that the 2-good-neighbor diagnosability of CΓ n under the PMC model and MM * model is g(n − 2) − 1, where n ≥ 4 and g is the girth of CΓ n .

“…So conditional diagnosability has been proposed by Lai et al in 2005 [23] by restricting that any node in the multiprocessor system must have a fault-free neighbor. The conditional diagnosability of various interconnection networks have been investigated [10], [11], [23]- [33]. In 2012, Peng et al proposed g-good neighbor conditional diagnosability as a generalization of the conditional diagnosability by assuming that any node in a multiprocessor system much have at least ggood neighbors [34].…”

mentioning

confidence: 99%

Hybrid Fault diagnosis capability analysis of Hypercubes under the PMC model and MM* model

Zhu¹,

Li²,

Liu³

et al. 2017

Preprint

System level diagnosis is an important approach for the fault diagnosis of multiprocessor systems. In system level diagnosis, diagnosability is an important measure of the diagnosis capability of interconnection networks. But as a measure, diagnosability can not reflect the diagnosis capability of multiprocessor systems to link faults which may occur in real circumstances. In this paper, we propose the definition of h-edge tolerable diagnosability to better measure the diagnosis capability of interconnection networks under hybrid fault circumstances. The h-edge tolerable diagnosability of a multiprocessor system G is the maximum number of faulty nodes that the system can guarantee to locate when the number of faulty edges does not exceed h,denoted by t e h (G). The PMC model and MM model are the two most widely studied diagnosis models for the system level diagnosis of multiprocessor systems. The hypercubes are the most well-known interconnection networks. In this paper, the h-edge tolerable diagnosability of n-dimensional hypercube under the PMC model and MM * is determined as follows: t e h (Qn) = n − h, where 1 ≤ h < n, n ≥ 3.