The Topology of Gaussian and Eisenstein-Jacobi Interconnection Networks

TitleThe Topology of Gaussian and Eisenstein-Jacobi Interconnection Networks
Publication TypeJournal Article
Year of Publication2010
AuthorsFlahive, M., and B. Bose
JournalIEEE Transactions on Parallel and Distributed Systems
Pagination1132 - 1142
Date Published08/2010
Keywordsdiameter of a network, Eisenstein-Jacobi integers, Gaussian integers, interconnection network, routing in networks

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.

Short TitleIEEE Trans. Parallel Distrib. Syst.