超立方体中最短和次短的点不交路径

Node-Disjoint Shortest and Next-to-Shortest Paths in N-Dimensional Hypercube

n维超立方体在并行计算领域有着广泛的应用,其特殊的拓扑结构对大规模的多处理器系统的性能具有重要的影响。本文研究n维超立方体Qn的最短路径问题,采用构造的方法证明了以下结论: Qn中任意两点之间一定存在k条不交的长度为k的最短路径,其中k为此两点之间的Hamming距离。此外,如果放宽最短路径的条件,对两点之间的 Hamming 距离为k的点,长度最多为k+2的不交路径存在至少n条。

N-dimensional hypercube is widely used in the field of parallel computer systems. The special topological structure of n-dimensional hypercube has significantly affected the performance of large multiprocessor systems. In this article, we prove the following result: In n-dimensional hypercube, for any two nodes with hamming distance that equals to k, there are k node-disjoint shortest paths of length k. Additionally, if we include nest-to-shortest paths of length k + 2 in addition to shortest paths, there will be n node-disjoint paths in total.