Issue No.08 - August (2010 vol.21)
Mary Flahive , Oregon State University, Corvallis
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TPDS.2009.132
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.
Interconnection network, Gaussian integers, Eisenstein-Jacobi integers, routing in networks, diameter of a network.
Mary Flahive, "The Topology of Gaussian and Eisenstein-Jacobi Interconnection Networks", IEEE Transactions on Parallel & Distributed Systems, vol.21, no. 8, pp. 1132-1142, August 2010, doi:10.1109/TPDS.2009.132