Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model

TL;DR

This paper investigates the fault diagnosis capabilities of bubble sort graphs in multiprocessor systems, introducing a new conditional diagnosability metric that significantly improves fault detection reliability.

Contribution

It establishes the conditional diagnosability of bubble sort graphs under the PMC model as 4n-11 for n ≥ 4, a notable enhancement over traditional diagnosability measures.

Findings

Conditional diagnosability is about four times the ordinary diagnosability.

The paper provides a precise formula for bubble sort graphs' fault tolerance.

Enhances understanding of fault diagnosis in large multiprocessor systems.

Abstract

As the size of a multiprocessor system increases, processor failure is inevitable, and fault identification in such a system is crucial for reliable computing. The fault diagnosis is the process of identifying faulty processors in a multiprocessor system through testing. For the practical fault diagnosis systems, the probability that all neighboring processors of a processor are faulty simultaneously is very small, and the conditional diagnosability, which is a new metric for evaluating fault tolerance of such systems, assumes that every faulty set does not contain all neighbors of any processor in the systems. This paper shows that the conditional diagnosability of bubble sort graphs $B_n$ under the PMC model is $4n-11$ for $n \geq 4$, which is about four times its ordinary diagnosability under the PMC model.