Quotients of Gaussian graphs and their application to perfect codes
Journal of Symbolic Computation
Energy-aware routing in hybrid optical network-on-chip for future multi-processor system-on-chip
Proceedings of the 6th ACM/IEEE Symposium on Architectures for Networking and Communications Systems
Energy-aware routing in hybrid optical network-on-chip for future multi-processor system-on-chip
Journal of Parallel and Distributed Computing
Frobenius circulant graphs of valency six, Eisenstein-Jacobi networks, and hexagonal meshes
European Journal of Combinatorics
Dense bipartite circulants and their routing via rectangular twisted torus
Discrete Applied Mathematics
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In this paper we consider a broad family of toroidal networks, denoted as Gaussian networks, which include many previously proposed and used topologies. We will define such networks by means of the Gaussian Integers, the subset of the Complex numbers with integer real and imaginary parts. Nodes in Gaussian networks are labeled by Gaussian integers, which confer these topologies an algebraic structure based on quotient rings of the Gaussian integers. In this sense, Gaussian integers reveal themselves as the appropriate tool for analyzing and exploiting any type of toroidal network. Using this algebraic approach, we can characterize the main distance-related properties of Gaussian networks, providing closed expressions for their diameter and average distance. In addition, we solve some important applications, like unicast and broadcast packet routing or the perfect placement of resources over these networks.