Reliability evaluation of half hypercube networks

Abstract

With the increase of the number of processors in the interconnection network, the failure of processors is inevitable. When the processor fails, the information passing through the failed processor will be unreliable, which may cause fatal consequences. Therefore, the research on the reliability of interconnection networks is an important topic, and the reliability of networks can be characterized by connectivity and diagnosability. In this paper, we first establish that the h-extra connectivity of the n-dimensional half hypercube network HHn is κh(HHn)=−12h2+(⌈n/2⌉−12)h+⌈n/2⌉+1 for n≥7 and 0≤h≤⌈n/2⌉−4, and then determine that the h-extra diagnosability of the HHn under the PMC model (n≥7 and 0≤h≤⌈n/2⌉−4) and the MM* model (n≥7 and 0≤h≤⌈n/2⌉4−1) is th(HHn)=−12h2+(⌈n/2⌉+12)h+⌈n/2⌉+1. Finally, we obtain that HHn is [−12k2+(⌈n/2⌉−12)k+⌈n/2⌉+1]/k-diagnosable under the PMC model.