Information flow and interconnections in computing: extensions and applications of Rent's rule

Abstract

Rent’s rule and related concepts of connectivity such as dimensionality, line-length distributions, and separators are discussed. Generalizations for systems for which the Rent exponent is not constant throughout the interconnection hierarchy are provided. The origin of Rent’s rule is stressed as resulting from the embedding of a high-dimensional information flow graph to two- or three-dimensional physical space. The applicability of these concepts to free-space optically interconnected systems is discussed. The role of Rent’s rule in fundamental studies of different interconnection media, including superconductors and optics, is briefly reviewed.