Narrow Results

A hypercube is an important interconnection topology in parallel and distributed processing. This paper treats fault tolerance of a hypercube. More precisely, it discusses relations between a faulty hypercube and its fault-free subcubes. First, this paper presents an upper bound on the minimum number of faults in an n-cube where no fault-free (n - m)-subcube can exist. Next, it is shown that the bound can be improved if m = 2. Finally, the paper discusses the number of faults when there are always at least two fault-free disjoint (n - 2)-subcubes.