Algorithms and optic implementation for reconfigurable networks

A model for reconfigurable networks is presented in a formal setting with respect to the general underlying topologies. A reconfigurable network is superior to traditional communication (fixed-connection) networks and to several other communication and computation models only if the transmission time is constant, regardless of the number of switches and links through which the message has to pass in the underlying architecture. This is not the case for switches using semiconductors technology. A zero-latency optical implementation for such networks, using existing guided-optic devices, is proposed. To demonstrate the power of the model, algorithms and lower bounds for computing SUM and its variants are considered. It is shown, using simple underlying topologies, that a reconfigurable machine completes such computations faster than any other realizable model and many other nonrealizable models. In particular, it is shown how to compute ranking and how to sort N keys in constant time on the N × N × N reconfigurable cube.