Reliability of recursive concentrator

The inverse omega network possesses various attractive properties and its constituent node has a fixed degree independent of the system size. In this paper, a proof for a technique applied recursively to construct an N-input concentrator switching network which is similar in topology to the inverse omega network will be introduced. Also an examination of a reliable inverse omega network in the presence of any single node failure will be presented. The new configuration of the system ensures providing the same high performance results obtained before the failure. In this paper, we show how to check the possibility by the inverse omega network of any given connection set and list some of the general patterns passable by this network. We also show that the concentrate operation passable by the inverse omega network is just a special case of the more general alternate sequence operation.