Hypercube (HC) networks (N$=$2${}^n$) provide efficient communication for parallel-and-distributed computing (PDC) but the HC-based multi-processor (MP) system is costly and not scalable, while hierarchical hypercube (HHC) networks (N$=$2${}^n$, n$=$2${}^m$+m) are less expensive and more scalable. However, the traditional HHC-routing easily conflicts, especially when executing multiple tasks (k > 2${}^m$ nodes-per-task). In the past, the node-disjoint-path routing could be used to avoid the conflict but that reliable (S, D) routing limited S(source)$=$0. Later, the parallel N2N (node-to-node) disjoint-path was proposed for reliable routing but limited (m+1)/2 pairs-of-nodes. Therefore, this study proposes the generalized N2N shortest-path (SP) routing (with arbitrary S) and the parallel N2N SP-routing, based on our hypothesis “the shortest-path routing and the proper HHC-partitioning can avoid the HHC-conflict directly”. Next, our innovation and contribution are 1. the GCD (grouping of cross dual-cube) partitioning to solve the HHC-conflict for $k\le 2^{m+1}$ nodes-per-task, and 2. the SP-ATAPE (all-to-all personalized exchange) embedding on the HHC-MPs. The correctness of the SP-routing was proven and the ATAPE communication was experimented to validate our conflict solution. The ATAPE results confirmed that in any group the GCD mapping could make all tasks (k $=$ 2${}^{m+1}$ nodes-per-task), synchronized with the same control, working without the conflict.

超立方体（HC）网络（N$=$2${}^{ñ}$）可为并行和分布式计算（PDC）提供有效的通信，但是基于HC的多处理器（MP）系统成本高昂且无法扩展，而分层超立方体（HHC）网络（N$=$2${}^{ñ}$，n$=$2${}^{米}$+ m）价格便宜，可扩展性更高。但是，传统的HHC路由很容易发生冲突，尤其是在执行多个任务时（k > 2${}^{米}$每个任务节点数）。过去，可以使用节点不相交路径路由来避免冲突，但是可靠的（S，D）路由会限制S（源）$=$0.随后，提出了并行的N 2 N（节点到节点）不相交路径以实现可靠的路由，但限制了（m +1）/ 2个节点对。因此，本研究提出了广义N 2 N最短路径（SP）路由（具有任意S）和并行N 2 N SP路由，基于我们的假设“最短路径路由和适当的HHC分区可以避免直接与HHC冲突”。接下来，我们的创新和贡献是1.解决GHC（交叉双多维数据集的分组）分区，以解决HHC冲突。$ķ\le 2^{米+\mathrm{1个}}$每个任务节点，以及2.嵌入在HHC-MP上的SP-ATAPE（所有对所有个性化交换）。验证了SP路由的正确性，并通过ATAPE通信进行了实验以验证我们的冲突解决方案。ATAPE结果证实，在任何组中，GCD映射都可以完成所有任务（k $=$ 2${}^{米+\mathrm{1个}}$ 每个任务的节点数），与同一个控件同步，工作无冲突。