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In the next decade, the high-performance supercomputers will consist of several millions of CPUs. The interconnection networks in such supercomputers play an important role for achieving high performance. In this paper, we introduce the Metacube (MC), a versatile family of interconnection network that can connect an extremely large number of nodes with a small number of links per node and keep the diameter rather low. An MC network has a 2-level hypercube structure. An MC(k, m) network can connect 2 2 k m+k nodes with m + k links per node, where k is the dimension of the high-level hypercubes (classes) and m is the dimension of the low-level hypercubes (clusters). An MC is a symmetric network with short diameter, easy and efficient routing and broadcasting similar to that of the hypercube. However, the MC network can connect millions of nodes with up to 6 links per node. An MC(2, 3) with 5 links per node has 16,384 nodes and an MC(3, 3) with 6 links per node has 134,217,728 nodes. We describe the MC network's structure, topological properties, routing and broadcasting algorithms, and the Hamiltonian cycle embedding in the Metacube networks.

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In this paper, we present a parallel-array implementation of a new non-restoring square root algorithm (PASQRT

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A low-degree dual-cube was proposed as an alternative to the hypercubes. A dual-cube DC(m) has m + 1 links per node where m is the degree of a cluster (m-cube) and one more link is used for connecting to a node in another cluster. There are 2 m+1 clusters and hence the total number of nodes is 2 2m+1 in a DC(m). In this paper, by using Gray code, we show that there exists a faulty-free cycle containing at least 2 2m+1 − 2 f nodes with f ≤ m − 1 faulty nodes.