Study on BPC Permutation Ability and Fault Tolerant Ability of Hypercube Networks

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Dimensional communicable 2 subcubes allocation problems in faulty hypercubes are studied in this research. An n-cube is investigated on whether the faulty n-cube possesses 2 m-dimensional disjoint fault-free subcubes or not. Larger values of m is more efficient in practical uses, so the case of m=n-2 is first examined. By giving a property of "the number of faults on an n-cube in which there always exist at least two fault-free (n-2) -subcubes is not over n-1", we obtained a property of "The number of faults located on an n-cube in which there always exist at least two fault-free (n-i-2) -subcubes is not over 2^i (n-i+1) -2". Next, the number of disjoint paths between the two subcubes is investigated. This number suggests the maximum number of faults by which the communication between these subcubes is never cut off. Then, whether the communication between two fault-free subcubes is always available or not when these two fault-free subcubes exist was discussed. This discussion gives a solution to establish a system where a regular hypercube alogrithm executing in an (m+1) -subcube still be executed by two fault-free disjoint communicable m-subcubes without any degradation even if the (m+1) -subcube becomes faulty.