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 findings, we also observe a surprising amount of difference in the performance between distinct topologies of the same degree. 1 Introduction The past few years have seen a rise in popularity of multiprocessors using direct networks that span two or three dimensions. Such networks typically follow the topology of a two or three-dimensional mesh or torus. Although topologies other than the mesh have been studied for two-dimensiona..