The maximum dimensional fault-free subcube allocatable in faulty hypercube

The maximum dimensional subcube located in faulty hypercubes is studied in this paper. Most parallel algorithms can be formulated with the dimension n of the hypercube being a parameter of the algorithm. The reconfiguration problem in a hypercube reduces to finding the maximum dimensional fault-free subcube in the hypercube, that is, helps in achieving graceful and the most effective degradation of the system. The paper presents the maximum number of faults on an n-cube on which there always exists at least one fault-free (n-2)-subcube.