Three-Dimensional Network Topologies

This paper presents the derivation and performance results of several new three-dimensional topologies. Various transformations can be applied to the conventional six-neighbor mesh in order to construct these topologies, which vary both in number of neighbors (degree) and logical connectivity. Analysis shows that after normalization for constant pin-count, lower-degree topologies yield lower latencies for long messages on unloaded networks, while higher-degree topologies possess higher bandwidth capacities. Although simulation results generally verify these ndings, we also observe a surprising amount of diierence in the performance between distinct topologies of the same degree.