On sequential diagnosis of multiprocessor systems

Abstract

This paper considers the problem of sequential fault diagnosis for various multiprocessor systems. We propose a simple sequential diagnosis algorithm and show that the degree of sequential diagnosability of any system with N processors is at least Ω ( N ) . We also show upper bounds for various networks. These are the first nontrivial upper bounds for the degree of sequential diagnosability, to the best of our knowledge. Our upper bounds are proved in a unified manner, which is based on the very definition of sequential diagnosability. We show that a d-dimensional grid and torus with N vertices are sequentially O ( N d / ( d + 1 ) ) -diagnosable, and an N-vertex k-ary tree is O ( kN ) -diagnosable. Moreover, we prove that the degree of sequential diagnosability of an N-vertex hypercube is at least Ω ( N / log N ) and at most O ( N log log N / log N ) , and those of an N-vertex CCC, shuffle-exchange graph, and de Bruijn graph are Θ ( N / log N ) .