Two ranking schemes for efficient computation on the star interconnection network

A node ranking scheme provides the necessary structural view for developing algorithms on a network. We present two ranking schemes for the star interconnection network both of which allow constant time order preserving communication. The first scheme is based on a hierarchical view of the star network. It enables one to efficiently implement order preserving ASCEND/DESCEND class of algorithms. This class includes several important algorithms such as the Fast Fourier Transform (FFT) and matrix multiplication. The other ranking scheme gives a flexible pipelined view of the star interconnection network and provides a suitable framework for implementation of pipelined algorithms.