On a Class of Multistage Interconnection Networks

TLDR

The paper introduces a baseline network and a configuration concept to assess relationships among proposed multistage interconnection networks. The authors develop a configuration‑based routing algorithm that supports one‑to‑one, one‑to‑many, and full communication between terminals, including a conflict resolution scheme. They prove that several networks—including the data manipulator, flip network, omega network, indirect binary n‑cube, and regular SW banyan—are topologically equivalent, and discuss practical implications for future research.

Abstract

A baseline network and a configuration concept are introduced to evaluate relationships among some proposed multistage interconnection networks. It is proven that the data manipulator (modified version), flip network, omega network, indirect binary n-cube network, and regular SW banyan network (S = F = 2) are topologically equivalent. The configuration concept facilitates developing a homogeneous routing algorithm which allows one-to-one and one- to-many connections from an arbitrary side of a network to the other side. This routing algorithm is extended to full communication which allows connections between terminals on the same side of a network. A conflict resolution scheme is also included. Some practical implications of our results are presented for further research.