Optimally scaling permutation routing on reconfigurable linear arrays with optical buses

We present an optimal and scalable permutation routing algorithm for three reconfigurable models based on linear arrays that allow pipelining of information through an optical bus. Specifically, for any P⩽N, our algorithm routes any permutation of N elements on a P-processor model optimally in O(N/P) steps. This algorithm extends naturally to one for routing h-relations optimally in O(h) steps. We also establish the equivalence of the three models, LARPBS, LPB, and POB. This implies an automatic translation of algorithms (without loss of speed or efficiency) among these models