Programming the twisted-cube architectures

Abstract

A network is proposed that preserves all of the properties of the hypercube, but has a diameter which is only about half of that of the hypercube. This network is self-routing, in the sense that there is a simple distributed routing algorithm which guarantees optimal paths between any pair of vertices. This fact, together with other properties such as regularity, symmetry, high connectivity, and a simple recursive structure, implies that the multiply twisted cube is an alternative to the ordinary hypercube for massively parallel architectures. Single-input multiple-data stream algorithm were developed which utilize the new architecture. The multiply-twisted hypercube architecture can be used to profitably emulate the ordinary hypercube. Some of the basic properties of this network are discussed, the programming issues are emphasized, and it is shown that any hypercube algorithm can be mapped to run on the new architecture. In many cases this mapping results in a substantial reduction in the running time due to more efficient routing of data between processors.<>