Optimal aspect ratio and number of separable row/column buses for mesh-connected parallel computers

A two-dimensional mesh of PEs with separable row and column buses has been shown to be quite effective for semigroup, prefix, and a wide class of other parallel computations. The authors show how semigroup and prefix computations can be performed with the same asymptotic time complexity on meshes having separable buses for a subset of rows and columns. They find that with this basic arrangement, square grids are not optimal but that a hierarchical method of synthesizing large meshes builds optimal square meshes from rectangular submeshes. The time-complexity results are shown to correspond to those previously published when certain parameters of the design are fixed at special values.<>