Equivalence between SP2 high-performance switches and three-stage Clos networks

In this paper we prove the functional equivalence of SP2 switches and rearrangeable three-stage Clos networks. From this equality we derive results on routing communications in SP2 switches. The present an algorithm using centralized control which can route any permutation in one pass through SP2 switches, for various system sizes. Further, we present a distributed control algorithm which can route the important class of linear-complement permutations through SP2 switches. Our results not only highlight the capabilities of SP2 switches, but also demonstrate how to efficiently route permutations at the application level