On recurrent and recursive interconnection patterns

Abstract

A number of trivalent graphs, in particular variants of the cube-connected cycles and shuffle-exchange, have become popular as interconnection patterns for synchronous parallel computers. We consider highly-structured interconnection patterns that allow large parallel machines to be constructed from isomorphic copies of smaller ones, plus (perhaps) a few extra processors. If only a small number of extra processors are added, we call the interconnection pattern recurrent. If no extra processors are added, we call it recursive. We show that a constant-degree recursive interconnection pattern is, in a sense, not as versatile as the cube-connected cycles or shuffle-exchange, and we present a trivalent recurrent interconnection pattern that is.