Recursive-Cube-of-Rings (RCR) Revisited: Properties and Enhancement

TL;DR

This paper revisits the properties of recursive-cube-of-rings (RCR) graphs, corrects previous misunderstandings, and proposes enhanced Class-II RCR graphs with improved connectivity and symmetry for parallel computing applications.

Contribution

It provides rigorous proofs correcting earlier misconceptions about RCR properties and introduces new edge connecting rules to create more uniform and better-connected RCR graphs.

Findings

Corrected topological properties of RCR graphs

Proposed Class-II RCR with improved connectivity

Enhanced symmetry and uniform node degrees

Abstract

We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating examples, we have corrected previous misunderstandings on the topological properties of these graphs, including node degree, symmetry, diameter and bisection width. To fully harness the potential of structural regularity through RCR construction, new edge connecting rules are proposed. The modified graphs, referred to as {\it Class-II RCR}, are shown to possess uniform node degrees, better connectivity and better network symmetry, and hence will find better application in parallel computing.