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

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.

A general approach to deriving diagnosability results of interconnection networks*

“…Issues related to the g-good-neighbor diagnosability of the arrangement graphs have been addressed in [13,51]. The g-extra diagnosability, g ∈ {1, 2, 3}, of the arrangement graph in terms of the PMC model has also been derived in [44] by following a structure dependent approach.…”