Metacube—a versatile family of interconnection networks for extremely large-scale supercomputers

Abstract

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.

A Set-to-Set Disjoint Paths Routing Algorithm in Tori

“…From Lemmas 13,14,15,16,17,18,19, and 20, we can construct 2n disjoint paths between S and D in τ (n, k) = τ (n − 1, k) + O(kn + n 2 log n) time and the maximum path length is λ(n, k)…”

“…A similar approach has been discussed in various previous works [13,14]. For reference, a comparative summary of the topological properties of tori and other networks [15] is given in Table 1 (the network cost is the degree by diameter product). The approach followed in this paper is a divide-and-conquer one, relying on the recursive property of tori.…”

Hypercube Fault Tolerant Routing with Bit Constraint

“…Not only are hypercubes popular as interconnection network on their own, but they are also very popular as seed for advanced network topologies such as those employed by hierarchical interconnection networks (HINs). Hierarchical hypercubes [4,5,6,7], hierarchical cubic networks [8,9,10], metacubes [11,12], dual-cubes [13,14] are some examples.…”

A Routing Algorithm Solving the Container Problem in a Hypercube with Bit Constraint

“…Additionally, one should note that hypercubes are very popular as seed (i.e. sub-network) of more complex interconnection network topologies, especially those for hierarchical interconnection networks (HINs) with examples such as dual-cubes 4 , metacubes 5 , hierarchical hypercubes 6 and hierarchical cubic networks 7 .…”