A new policy to solve routing conflicts in shuffle-exchange networks

Batch routing is an important approach for solving routing conflicts in SE (shuffle-exchange) networks. However, the complexity of batching and the uncertainty of batch size makes this approach impracticable. Based on sequence division and routing coding concepts, we propose a method for detecting routing conflicts in an SE network, known as dividing detection that is more efficient than the method for window detection. In addition, a new conjecture relating to routing policies in SE networks is proposed. This is proved using a constructive approach when n < 6. Based on the conjecture, a new routing scheme for SE networks is provided. Using this scheme, all the input signals can be transfered without conflicts and within two batches, while the efficiency of the batch routing is noticeably improved.