Mixed Preservation of Conditionally Nonblocking Switches under 2-stage Interconnection

The 2-stage interconnection network is conceivably the most compact design for interconnecting small switches into a large switch. When a certain class of switches is preserved under 2-stage interconnection, recursive application of 2-stage interconnection then builds indefinitely large switches in this class from atomic ones. The present paper studies switches that are not preserved under 2-stage interconnection but are yet constructive from atomic elements through recursive 2-stage interconnection. The principle is "mixed preservation" based on the following two properties: first, the 2-stage interconnection network constructs a class-A switch when switches at nodes on one stage belong to class A and switches at nodes on the other stage belong to class B; second, class-B switches are preserved under 2-stage interconnection. A class of conditionally nonblocking switches for such mixed preservation are identified, which are useful in the recursive construction of distribution networks