The Recursive Dual-Net and Its Applications

In this paper, we propose a universal network, called recursive dual-net (RDN). It can be used as a candidate of effective interconnection networks for massively parallel computers. The RDN is generated by recursively applying dual-construction on a base-network. Given a regular and symmetric graph of size n and node-degree d, the dual-construction generates a regular and symmetric graph of size 2n and node-degree d+1. The RDN has many interesting properties including low node-degree and small diameter. For example, we can construct an RDN connecting more than 3-million nodes with only 6 links per node and a diameter of 22. We investigate the topological properties of the RDN and compare it to other networks including 3D torus, WKrecursive network, hypercube, cube-connected-cycle, and dual-cube. We also describe an efficient routing algorithm for RDN.