Fault Diagnosability of Arrangement Graphs

TL;DR

This paper analyzes the fault diagnosability of arrangement graphs, showing their high resilience to faults and establishing precise diagnosability bounds under the comparison model.

Contribution

It introduces the concept of fault resiliency in arrangement graphs and determines their conditional diagnosability for various parameters.

Findings

Largest connected component contains almost all vertices under certain fault conditions

Conditional diagnosability of $A_{n,k}$ is $(3k-2)(n-k)-3$ for $k extgreater=4$, $n extgreater=k+2$

Conditional diagnosability of $A_{n,n-1}$ is $3n-7$ for $n extgreater=5$

Abstract

The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and to replace the faulty processors to maintain a system's high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. This paper shows that the largest connected component of the survival graph contains almost all remaining vertices in the $(n,k)$-arrangement graph $A_{n,k}$ when the number of moved faulty vertices is up to twice or three times the traditional connectivity. Based on this fault resiliency, we establishes that the conditional diagnosability of $A_{n,k}$ under the comparison model. We prove that for $k\geq 4$, $n\geq k+2$, the conditional diagnosability of $A_{n,k}$ is $(3k-2)(n-k)-3$; the conditional diagnosability of $A_{n,n-1}$ is $3n-7$ for $n\geq 5$.