The generalized hypercube (GH) is one key interconnection network with excellent topological properties. It contains many other interconnection topologies, such as the hypercube network, the complete graph, the mesh network, and the $k$k-ary $n$n-cube network. It can also be used to construct some data center networks, such as HyperX, BCube, FBFLY, and SWCube. However, the construction cost of GH is high since it contains too many links. In this paper, we propose a novel low cost interconnection architecture called the exchanged generalized hypercube (EGH). We study the properties of EGH, such as the number of edges, the degree of vertices, connectivity, diameter, and diagnosability. Then, we give a routing algorithm to find the shortest path between any two distinct vertices of EGH. Furthermore, we design an algorithm to give disjoint paths between any two distinct vertices of EGH. In addition, we propose two local diagnosis algorithms: LDT$_{EGH}$EGH and LDWB$_{EGH}$EGH in EGH under PMC model and MM model, respectively. Simulation results demonstrate that even if the proportion of faulty vertices in EGH is up to 25 percent, the probability that these two diagnosis algorithms can successfully determine the status of vertices is more than 90 percent. As far as the number of edges is concerned, the analysis shows that the construction cost of EGH is much less than that of GH. We could regard this work as the basis for proposing future new high performance topologies.

中文翻译：

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一种基于广义超立方体的新型低成本互连架构

广义超立方体（GH）是一种具有优异拓扑特性的关键互连网络。它包含许多其他互连拓扑，例如超立方体网络、完全图、网状网络和$千$克-ary $n$n-多维数据集网络。也可用于构建一些数据中心网络，如HyperX、BCube、FBFLY、SWCube等。但是，GH的建设成本很高，因为它包含太多的环节。在本文中，我们提出了一种称为交换广义超立方体（EGH）的新型低成本互连架构。我们研究 EGH 的属性，例如边数、顶点度数、连通性、直径和可诊断性。然后，我们给出了一个路由算法来找到 EGH 的任意两个不同顶点之间的最短路径。此外，我们设计了一种算法来给出 EGH 的任何两个不同顶点之间的不相交路径。此外，我们提出了两种局部诊断算法：LDT$_{EGH}$乙GH 和LDWB$_{EGH}$乙GH分别在 PMC 模型和 MM 模型下的 EGH 中。仿真结果表明，即使EGH中错误顶点的比例高达25%，这两种诊断算法能够成功确定顶点状态的概率也超过90%。就边数而言，分析表明EGH的建设成本远低于GH。我们可以将这项工作视为提出未来新的高性能拓扑的基础。