An Algorithm for Constructing Hamiltonian Cycle in Metacube Networks

The high-performance supercomputers will consist of several millions of CPUs in the next decade. The interconnection networks (INs) in such supercomputers play an important role. Metacube (MC) is an attractive IN that can connect extremely large number of nodes with small number of links, meanwhile it holds a short diameter and keeps the simplicity of routing algorithm. An MC(k, m) network can connect 2^m2k+k nodes with m+k links per node, where k is the dimension of the high-level cubes (classes) and m is the dimension of the low-level cubes (clusters). For example, an MC(3,3) with 6 links per node can connect 2²⁷, or 134,217,728, nodes. In this paper, we show that the Metacube is Hamiltonian and give an efficient algorithm to construct a Hamiltonian cycle in Metacube networks.