Swapped interconnection networks: Topological, performance, and robustness attributes

Interconnection architectures range from complete networks, that have a diameter of D=1 but are impractical except when the number n of nodes is small, to low-cost, minimally connected ring networks whose diameter D=⌊n/2⌋ is unacceptable for large n. In this paper, our focus is on swapped interconnection networks that allow systematic construction of large, scalable, modular, and robust parallel architectures, while maintaining many desirable attributes of the underlying basis network comprising its clusters. A two-level swapped network with n2 nodes is built of n copies of an n-node basis network using a simple rule for intercluster connectivity (node j in cluster i connected to node i in cluster j) that ensures its regularity, modularity, packageability, fault tolerance, and algorithmic efficiency. We show how key parameters of a swapped interconnection network are related to the corresponding parameters of its basis network and discuss implications of these results to synthesizing large networks with desirable topological, performance, and robustness attributes. In particular, we prove that a swapped network is Hamiltonian (respectively, Hamiltonian-connected) if its basis network is Hamiltonian (Hamiltonian-connected). These general results supersede a number of published results for specific basis networks and obviate the need for proving Hamiltonicity or Hamiltonian connectivity for many other basis networks of practical interest.