Abstract
OTIS networks are interconnection networks amenable to deployment as hybrid networks containing both electronic and optical links. Deficiencies as regards symmetry led to the subsequent formulation of biswapped networks which were later generalized to multiswapped networks so as to still enable optoelectronic implementation (as it happens, multiswapped networks also generalize previously studied hierarchical crossed cubes). Multiswapped networks of the form Msw(H;G) are known to possess good (graph-theoretic) properties as regards their use as (optoelectronic) interconnection networks (in distributed-memory multiprocessors) and in relation to those of the component networks G and H. Combinatorially, they provide a hierarchical mechanism to define new networks from existing networks (so that the properties of the new network can be controlled in terms of the constituent networks). In this paper, we prove that if G and H are Hamiltonian networks then the multiswapped network Msw(H;G) is also Hamiltonian. At the core of our proof is finding specially designed Hamiltonian cycles in 2-dimensional and heavily pruned 3-dimensional tori, irrespective of the actual networks G and H we happen to be working with. This lends credence to the role of tori as fundamental networks within the study of interconnection networks.
Highlights
Interconnection networks are used to interconnect the processors of a distributed-memory multiprocessor computer as well as within networks-onchip, cluster computers and data centres
An influential paper was [28] where a deadlock-free path-based multicast wormhole routing algorithm for distributed-memory multiprocessors was devised, with the freedom from deadlock stemming from the existence and use of a Hamiltonian cycle embedded within the interconnection network; this paper has inspired a range of related research
We have demonstrated that multiswapped networks provide a mechanism for graph composition, as well as further demonstrating the efficacy of multiswapped networks as interconnection networks for parallel computing
Summary
Interconnection networks are used to interconnect the processors of a distributed-memory multiprocessor computer (such as a Cray Jaguar or an IBM Blue Gene) as well as within networks-onchip, cluster computers and data centres (it is primarily the combinatorics related to the former usage that concerns us in this paper). Some of the graph-theoretic properties of Msw(H; G) studied in [38] involve the lengths of shortest paths joining any two nodes, the diameter, the connectivity, the fault-diameter and node symmetry. All of these properties are highly relevant with regard to the use of multiswapped networks as (optoelectronic) interconnection networks but they hint as to the naturalness of Msw(H; G) as a method of graph composition. We continue with the development of multiswapped networks both as providing the topologies of potential interconnection networks and as a generic mechanism for graph composition (we highlight later how multiswapped networks might be relevant to the design of data centre networks). In order to emphasize the architectural origins of our graphs, we often refer to graphs as networks (though we use the two terms interchangeably) and we always refer to vertices as nodes and (undirected) edges as links
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