Manipulating Multistage Interconnection Networks Using Fundamental Arrangements

Abstract: Optimizing interconnection networks is a prime object in switching schemes. In this work the authors present a novel approach for obtaining a required channel arrangement in a multi-stage interconnection network, using a new concept - a fundamental arrangement. The fundamental arrangement is an initial N-1 stage switch arrangement that allows obtaining any required output channel arrangement given an input arrangement, using N/2 binary switches at each stage. The paper demonstrates how a fundamental arrangement can be achieved and how, once this is done, any required arrangement may be obtained within 2(N-1) steps.