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

Shiying Wang,Yunxia Ren

doi:10.3390/info9110275

Abstract

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.

Highlights

A multiprocessor system and interconnection network has an underlying topology, which is usually presented by a graph, where nodes represent processors and links represent communication links between processors
Some processors may fail in the system, so processor fault identification plays an important role for reliable computing
In 2012, Peng et al [6] proposed a measurement for fault diagnosis of the system G, namely, the g-good-neighbor diagnosability t g ( G ), which requires that every fault-free node has at least

Summary

Introduction

A multiprocessor system and interconnection network (networks for short) has an underlying topology, which is usually presented by a graph, where nodes represent processors and links represent communication links between processors. Several diagnosis models were proposed to identify the faulty processors. In 2005, Lai et al [3] introduced a measurement for fault diagnosis of a system, namely, the conditional diagnosability. They considered the situation that no fault set can contain all the neighbors of any vertex in the system. In 2012, Peng et al [6] proposed a measurement for fault diagnosis of the system G, namely, the g-good-neighbor diagnosability t g ( G ) (which is called the g-good-neighbor conditional diagnosability), which requires that every fault-free node has at least. In [6], they studied the g-good-neighbor diagnosability of the n-dimensional hypercube under the PMC model.

Preliminaries

The arrangement

The g-Good-Neighbor Diagnosability of Arrangement Graphs under the PMC Model

Conclusions