In this paper, a new two-level interconnection network, called a hierarchical folded-hypercube network (HFN, for short), is proposed. The HFN takes folded hypercubes as basic modules which are connected in a complete manner. We investigate the topological properties of the HFN, including the diameter, cost, average distance, embedding, connectivity, container, rc-wide diameter, and node-fault diameter. We show that the HFN can emulate algorithms which are executable on the ring or the mesh-connected computer with the same time complexities in big-0 notation. Moreover, the HFN can embed a folded hypercube having the same number of nodes with constant dilation. We compute the diameter, node connectivity, best container, K-wide diameter, and node-fault diameter of the HFN. We present optimal routing and broadcasting algorithms for the HFN. The semigroup computation and descendascend algorithms can be executed as well on the HFN.
Recently, with the support of the CAPRI (Concurrent Architecture and PRogramming environment for highly Integrated system) project, Vecchia and Sanges proposed a new general class of recursively scalable networks, termed WK-recursive networks, and developed routing and broadcasting algorithms on them. They have also implemented the WK-recursive networks using VLSl technology. This paper studies WK-recursive networks by first investigating their topological properties such as diameter, connectivity, and Hamiltonicity. We then develop new and more efficient routing and broadcasting algorithms. Our routing algorithm can guarantee the shortest paths. Our broadcasting algorithm is much simpler and requires fewer extra bits to be transmitted. The broadcasting tree of our broadcasting algorithm is of minimal height (equal to the diameter), and each node receives the message exactly once. Moreover, we show the execution of descend/ ascend algorithms on the WK-recursive networks using the bitonic sort as an illustrative example.
An n-dimensional hierarchical cubic network [denoted by HCN(n)] contains 2 n n-dimensional hypercubes. The diameter of the HCN(n), which is equal to n ؉ (n ؉ 1)/3 ؉ 1, is about two-thirds the diameter of a comparable hypercube, even though it uses about half as many links per node. In this paper, a maximal number of nodedisjoint paths are constructed between every two distinct nodes of the HCN(n). Their maximal length is bounded above by n ؉ n/3 ؉ 4, which is nearly optimal. The (n ؉ 1)-wide diameter and n-fault diameter of the HCN(n) are shown to be n ؉ n/3 ؉ 3 or n ؉ n/3 ؉ 4, which are about two-thirds those of a comparable hypercube. Our results reveal that the HCN(n) has a smaller wide diameter and fault diameter than those of a comparable hypercube.
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