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Folded Petersen cube networks: new competitors for the hypercubes

机译：折叠式Petersen多维数据集网络：超多维数据集的新竞争者

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摘要

We introduce and analyze a new interconnection topology, called the k-dimensional folded Petersen (FP/sub k/) network, which is constructed by iteratively applying the Cartesian product operation on the well-known Petersen graph. Since the number of nodes in FP/sub k/ is restricted to a power of ten, for better scalability we propose a generalization, the folded Petersen cube network FPQ/sub n,k/=Q/sub n//spl times/FP/sub k/, which is a product of the n-dimensional binary hypercube (Q/sub n/) and FP/sub k/. The FPQ/sub n,k/ topology provides regularity, node- and edge-symmetry, optimal connectivity (and therefore maximal fault-tolerance), logarithmic diameter, modularity, and permits simple self-routing and broadcasting algorithms. With the same node-degree and connectivity, FPQ/sub n,k/ has smaller diameter and accommodates more nodes than Q/sub n+3k/, and its packing density is higher compared to several other product networks. This paper also emphasizes the versatility of the folded Petersen cube networks as a multicomputer interconnection topology by providing embeddings of many computationally important structures such as rings, multi-dimensional meshes, hypercubes, complete binary trees, tree machines, meshes of trees, and pyramids. The dilation and edge-congestion of all such embeddings are at most two.
机译：我们介绍并分析了一种新的互连拓扑，称为k维折叠式Petersen（FP / sub k /）网络，该拓扑是通过在著名的Petersen图上迭代应用笛卡尔乘积运算而构造的。由于FP / sub k /中的节点数被限制为10的幂，因此为了获得更好的可伸缩性，我们提出了一种概括，即折叠的Petersen立方体网络FPQ / sub n，k / = Q / sub n // spl times / FP / sub k /，它是n维二进制超立方体（Q / sub n /）和FP / sub k /的乘积。 FPQ / sub n，k /拓扑提供规则性，节点和边缘对称性，最佳连接性（并因此具有最大的容错性），对数直径，模块化，并允许简单的自路由和广播算法。在相同的节点度和连通性的情况下，FPQ / sub n，k /的直径较小，并且与Q / sub n + 3k /相比，可容纳更多的节点，并且其包装密度比其他几个产品网络更高。本文还通过提供许多重要计算结构的嵌入，例如环，多维网格，超立方体，完整的二叉树，树机器，树网格和金字塔，强调了折叠式Petersen多维数据集网络作为多计算机互连拓扑的多功能性。所有这些嵌入的扩张和边缘拥塞最多为两个。

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