The Topology of Gaussian and Eisenstein-Jacobi Interconnection Networks

Authors:
Mary Flahive;Bella Bose
Affiliations:
Oregon State University, Corvallis;Oregon State University, Corvallis
Venue:
IEEE Transactions on Parallel and Distributed Systems
Year:
2010

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Abstract

Earlier authors have used quotient rings of Gaussian and Eisenstein-Jacobi integers to construct interconnection networks with good topological properties. In this paper, we present a unified study of these two types of networks. Our results include decomposing the edges into disjoint Hamiltonian cycles, a simplification of the calculation of the Eisenstein-Jacobi distance, a distribution of the distances between Eisenstein-Jacobi nodes, and shortest path routing algorithms. In particular, the known Gaussian routing algorithm is simplified.