Work-preserving emulations of shuffle-exchange networks: An analysis of the complex plane diagram

In this paper we show that for each n, the order-n shuffle-exchange network can be emulated by an n-node linear processor array or an n²-node mesh in a work-preserving manner. An emulation of a computation on a guest network is work-preserving on a host network , if the time-processor products are equal to within a constant factor. To achieve this result we demonstrate a uniform many-to-one embedding of the nodes of a shuffle-exchange network into a linear array. We then give a simple, deterministic routing algorithm on the linear array which schedules the communication of messages necessary to achieve the emulation within the required time bounds. The analysis of the algorithm relies on certain statistical properties of the complex plane diagram of the shuffle-exchange network.