Quotient rings of Gaussian and Eisenstein-Jacobi(EJ) integers can be deployed to construct interconnection networks with good topological properties. In this thesis, we propose deadlock-free deterministic and partially adaptive routing algorithms for hexagonal networks, one special class of EJ networks. Then we discuss higher dimensional Gaussian networks as an alternative to classical multidimensional toroidal networks. For this topology, we explore many properties including distance distribution and the decomposition of higher dimensional Gaussian net works into Hamiltonian cycles. In addition, we propose some efficient communication algorithms for higher dimensional Gaussian networks including one-to-all broadcasting and shortest path routing. Simulation results show that the routing algorithm proposed for higher dimensional Gaussian networks outperforms the routing algorithm of the corresponding torus networks with approximately the same number of nodes. These simulation results are expected since higher dimensional Gaussian networks have a smaller diameter and a smaller average message latency as compared with toroidal networks.
Finally, we introduce a degree-three interconnection network obtained from pruning a Gaussian network. This network shows possible performance improvement over other degree-three networks since it has a smaller diameter compared to other degree-three networks. Many topological properties of degree-three pruned Gaussian network are explored. In addition, an optimal shortest path routing algorithm and a one-to-all broadcasting algorithm are given