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

研究了故障超立方体中维度可传播2个子立方体的分配问题。研究了一个n-立方体是否存在2m维不相交的无故障子立方体。在实际应用中，m的值越大越有效，因此首先考察m=n-2的情况。通过给出“n-立方体上总存在至少两个无故障(n-2)-子立方体的故障个数不超过n-1”的性质，得到了“总存在至少两个无故障(n-i-2)-子立方体的n-立方体上的故障个数不超过2^i(n-i+1)-2”的性质。其次，研究了两个子立方体之间不相交路径的数目。这个数字表明这些子多维数据集之间的通信永远不会中断的最大故障数。然后，讨论了当两个无故障子立方体存在时，这两个无故障子立方体之间的通信是否始终可用。给出了建立这样一个系统的解决方案：在一个(m+1)-子立方体中执行的正则超立方体算法仍然由两个无故障的不相交的可通信m-子立方体执行，即使(m+1)-子立方体出现故障，也不会有任何退化。

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.