Diagnosability for two families of composition networks

Abstract

Diagnosability is an important parameter to assess the reliability of multiprocessor systems. A multiprocessor system is called t-diagnosable if all faulty processors can be identified without replacement as long as the number of faulty processors does not exceed t. The diagnosability is the maximum value of t such that multiprocessors system is t-diagnosable. Matching composition networks (MCNs) and cycle composition networks (CCNs) are two typical network structures to construct multiprocessor systems. Let G be a MCN which is obtained by adding a perfect matching between two graph G0 and G1, and let H be a CCN obtained by adding a perfect matching between Gi and Gi+1(modm) for each i∈{0,1,…,m−1} with m≥3. In this paper, we show that the diagnosability of G under the PMC (δ(G)≥2) model and MM⁎ model (δ(G)≥5) is n−1 if G0≅G1≅Kn; otherwise, δ(G). Furthermore, we show that the diagnosability of H under the PMC model (δ(H)≥4) and MM⁎ model (δ(H)≥5) is δ(H).