High diagnosability of a sequential diagnosis algorithm in hypercubes under the PMC model

Abstract

We consider the problem of sequential fault diagnosis in a hypercube multiprocessor system under the PMC model. The diagnosability is defined as the ability to provide a correct and complete diagnosis. In this paper, we propose a novel and simple sequential diagnosis method called the MajorAggregate (MA) algorithm, which is based on the idea of vertex-isoperimetric inequality for hypercubes and consists of two phases. Moreover, we define the minimum cut-set to partition the whole hamming sphere of hypercube into three parts, minimum cut-set itself, and two isolated aggregates. From the worst case, the value of minimum cut-set size is assigned to t value, diagnosability. In the algorithm, after identifying a subset, major aggregate, of connected fault-free nodes, MA regards its boundary nodes as faulty and then proceeds the iterations of diagnosis and repair. Then, we prove the lower bound to diagnosability in the scheme is \(\Omega( \frac{2^{d}}{\sqrt{d}} )\) for a d-dimensional hypercube. This result obviously improves the best lower bound of diagnosability, \(\Omega( \frac{2^{d}\log d}{d} )\), in previous researches.